I've just read some of that Taibbi article and it's either badly researched, or it's deliberately misleading.
First, the passage from the article I'm going to talk about:
This failure to demand specifics has been epidemic in Russiagate, even when good reporters have been involved. One of the biggest “revelations” of this era involved a story that was broken first by a terrible reporter (the Guardian’s Luke Harding) and followed up by a good one (Jane Mayer of the New Yorker). The key detail involved the elusive origin story of Russiagate.
Mayer’s piece, the March 12, 2018 “Christopher Steele, the Man Behind The Trump Dossier” in the New Yorker, impacted the public mainly by seeming to bolster the credentials of the dossier author. But it contained an explosive nugget far down. Mayer reported Robert Hannigan, then-head of the GCHQ (the British analog to the NSA) intercepted a “stream of illicit communications” between “Trump’s team and Moscow” at some point prior to August 2016. Hannigan flew to the U.S. and briefed CIA director John Brennan about these communications. Brennan later testified this inspired the original FBI investigation.
When I read that, a million questions came to mind, but first: what did “illicit” mean?
If something “illicit” had been captured by GCHQ, and this led to the FBI investigation (one of several conflicting public explanations for the start of the FBI probe, incidentally), this would go a long way toward clearing up the nature of the collusion charge. If they had something, why couldn’t they tell us what it was? Why didn’t we deserve to know?
I asked the Guardian: “Was any attempt made to find out what those communications were? How was the existence of these communications confirmed? Did anyone from the Guardian see or hear these intercepts, or transcripts?”
Their one-sentence reply:
The Guardian has strict and rigorous procedures when dealing with source material.
That’s the kind of answer you’d expect from a transnational bank, or the army, not a newspaper.
The first thing to note, is that Taibbi seems to be trying to give the impression that Mayer got the word "illicit" from Harding, but that's not true.
This is Harding's piece (co-authored with two other people) and it doesn't use the word "illicit", and nor does it try to paint the communications as illicit. This is what it says:
GCHQ first became aware in late 2015 of suspicious “interactions” between figures connected to Trump and known or suspected Russian agents, a source close to UK intelligence said. This intelligence was passed to the US as part of a routine exchange of information, they added.
Over the next six months, until summer 2016, a number of western agencies shared further information on contacts between Trump’s inner circle and Russians, sources said.
The European countries that passed on electronic intelligence – known as sigint – included Germany, Estonia and Poland. Australia, a member of the “Five Eyes” spying alliance that also includes the US, UK, Canada and New Zealand, also relayed material, one source said.
Another source suggested the Dutch and the French spy agency, the General Directorate for External Security or DGSE, were contributors.
It is understood that GCHQ was at no point carrying out a targeted operation against Trump or his team or proactively seeking information. The alleged conversations were picked up by chance as part of routine surveillance of Russian intelligence assets. Over several months, different agencies targeting the same people began to see a pattern of connections that were flagged to intelligence officials in the US.
Note that they're described as "suspicious", rather than "illicit".
It's also worth noting that Taibbi frames these communications as being of a nature which can be heard or transcribed. However, there is nothing in Harding's article that implies this. Indeed, they're referred to as "interactions", "contacts", "surveillance", "alleged conversations", and "connections". None of that implies that any conversations were recorded or transcribed. Indeed, it was later reported (in an article that doesn't come immediately to hand and which I don't have time to find right now) that the nature of the interceptions was simply the agencies monitoring who had been in contact with the agents they were surveilling, rather than actually intercepting any calls. In other words, it's the equivalent of looking at their phone bills to see what numbers there are on there.
In fact, Taibbi doesn't seem to know about this April 2017 article at all, and instead refers to
this Nov 2017 article as being where "the story had originally been broken".* That article, one portion of which briefly summarises the earlier article, naturally contains far less information or detail:
In late 2015 the British eavesdropping agency, GCHQ, was carrying out standard “collection” against Moscow targets. These were known Kremlin operatives already on the grid. Nothing unusual here – except that the Russians were talking to people associated with Trump. The precise nature of these exchanges has not been made public, but according to sources in the US and the UK, they formed a suspicious pattern. They continued through the first half of 2016. The intelligence was handed to the US as part of a routine sharing of information.
The FBI and the CIA were slow to appreciate the extensive nature of these contacts between Trump’s team and Moscow. This was in part due to institutional squeamishness – the law prohibits US agencies from examining the private communications of US citizens without a warrant.
But the electronic intelligence suggested Steele was right. According to one account, the US agencies looked as if they were asleep. “‘Wake up! There’s something not right here!’ – the BND [German intelligence], the Dutch, the French and SIS were all saying this,” one Washington-based source told me.
That summer, GCHQ’s then head, Robert Hannigan, flew to the US to personally brief CIA chief John Brennan. The matter was deemed so important that it was handled at “director level”, face-to-face between the two agency chiefs. James Clapper, director of national intelligence, later confirmed the “sensitive” stream of intelligence from Europe. After a slow start, Brennan used the GCHQ information and other tip-offs to launch a major inter-agency investigation.
He notes here that the nature of the exchanges haven't been made public but, again, that it was the pattern that was suspicious. And, once more, the word "illicit" is nowhere to be found.
And if anybody is thinking that Tiabbi is not implying that "illicit" was Harding's word, then the following quote re Mayer should make it clear:
I can only infer she couldn’t find out what “illicit” meant despite proper effort.
He concludes this segment by saying:
To be clear, I don’t necessarily disbelieve the idea that there were “illicit” contacts between Trump and Russians in early 2015 or before. But if there were such contacts, I can’t think of any legitimate reason why their nature should be withheld from the public.
Leaving aside the fact that he appears to be suggesting that it's Harding who is withholding information about this, rather than the intelligence agencies themselves, this is nothing but an argument from incredulity. That Taibbi can't think of any legitimate reason could just as easily imply a lack of imagination, understanding, or knowledge on his part - or even intentional disingenuity - as it could bad journalism or malfeasance on Harding's. It's a logical fallacy and a meaningless, content-less statement.
I'm sure I could get into much more from this article, if I had the time or inclination to chase everything up, but this part just leapt out at me because I remembered the actual Guardian story quite well and Taibbi's characterisation of it immediately seemed off. The impression I'm getting, though, is that this article is as bad journalistically as he is claiming the journalism he's commenting on is. It seems to me that this is even more egregious if it's not an article he's written to a tight deadline due to the news about Mueller, but instead the chapter of a book.
*It's difficult to tell whether Mayer told him that she used Harding as her source and Taibbi independently found the article he thought it must have been, or if she cited this particular article and he didn't check whether or not that was where the story was actually originally broken.