You are describing a version of what is sometimes called the Weak Anthropic Principle (WAP). This principle takes as a given that the constants required for live to exist (size of gravity force, size of electromagnetic force, size of nuclear weak force, balance of positive and negative charge, and many more!) are extremely well-tuned for life as it exists. However the Weak Anthropic Principle is that this is not evidence that they were created that way by an intelligent Creator. The Weak Anthropic Principle simply acknowledges the fantastic coincidence that all these parameters happen to have the right value for life to exist, but they deny that this is evidence of a purpose behind this fact. Those who propose that life adapted to the universe rather than vice versa probably will find themselves in the WAP camp.
To me this comes close to being a silly argument. Here is why. If the gravity force was not tuned to one part in 10 to the 60th power, then galaxies, stars and planets would not have formed. How could life exist if there were not stars and planets? Life cannot adapt to a different gravity force. Wrong gravity force, no life. That is the end of the story. Take the nuclear strong force, which is what attracts neutrons and protons. If this value were to change by about 5% in either direction, then there would either be all hydrogen and no other elements (if it were 5% weaker) or there would be no hydrogen at all (if it were 5% stronger). How could life adapt to a universe with either all hydrogen or no hydrogen? Again, this makes no sense. As far as I know, either ALL of the fine tuning or at the very least nearly all of the fine tuning falls into this category. In other words, it is absolutely impossible for life to adapt to itself to a universe almost EXACTLY the same as the one we happen to live in. This claim is incontrovertible. A couple more examples: If the amount of positive and negative charge were not fantastically fine-tuned, then molecules would not exist. If molecules did not exist, then life also would not exist. To be honest with you, anyone who makes this proposal is either completely ignorant of the facts underlying the fine tuning argument or is purposefully obfuscating on this question. To me, this argument appears downright silly. Those atheists who throw this idea around had better do some explaining how life can exist in a universe without the nuclear weak, nuclear strong, electromagnetic and gravity forces extremely fine-tuned. They cannot! And many more examples can be given.
I agree with you, that if we do not find some sort of work-around to the strong anthropic principle, then we are left with the non-scientific infinite universe theory. The “puddle” analogy does not work. The universe is tuned for life, not life for the universe. Therefore, atheists have proposed the infinite universe theory. This theory is not scientific for two reasons. First, it is an irrefutable hypothesis. A hypothesis which cannot be refuted by any conceivable experiment is not scientific and the multiverse theory has this unfortunate property. Second, the theory is not only not supported by any evidence, it is literally impossible to supply any scientific evidence for this hypothesis. It is an ad hoc hypothesis–ie the idea was created, not because of any evidence or any scientific imperative, but simply as a convenient way to respond to the anthropic principle (either the strong or the weak variety). I agree with you, the multiverse theory is a massive stretch. But then it is not as big a stretch as using the “puddle analogy” to refute the teleological argument.