That's the closest that you've come to accurately assessing the analogy! Progress! There's still a bit more, though, such as the implication that there's likely more than one possible shape that the puddle could be and still be wondering about how it fit so well.

The puddle represents any beings in a similar position to humans, not just humans, after all. A similar view is quite expectable to arise in pretty much any intelligent species.
Ahh. You just don't like accepting uncomfortable labels, no matter how accurate. That's not a failure of the analogy, though.
Sure. Of note, though, it does not imply that all puddles are sapient. Rather, it simply points out that that all sapient puddles would be in a position where they find that the hole perfectly matches the puddle.
Again, your attempt to reframe things just doesn't work. This is, again, not a failure of the analogy, given that you're trying to invoke entirely different principles, and ones that are not validly backed up, at that. Again, a sample size of 1 does not give sufficient data to reasonably make any conclusions about a range of potential values. The "scientific" calculations that you want to invoke are the products of attempts to figure out how things work and the overwhelming majority of the attempts are simply wrong, and we don't know which, if any, of the current options are reasonable to actually consider to be right.
Got any real objections?