The assumption here seems to be that sentient life must necessarily be carbon-based. This could well be true, but how could one ever know that for sure?
We can't. This is a common misconception. The position comes from a weak understanding of biochemistry, forming the basis of carbon chauvinism. From the Wikipedia article:
In a 1999 Reason magazine article discussing the theory of a
fine-tuned universe, Kenneth Silber quotes astrophysicist Victor J.
Stenger using the term:
There is no good reason, says Stenger, to
"assume that there's only one kind of life possible" - we know far too
little about life in our own universe, let alone "other" universes, to
reach such a conclusion. Stenger denounces as "carbon chauvinism" the
assumption that life requires carbon; other chemical elements, such as
silicon, can also form molecules of considerable complexity. Indeed,
Stenger ventures, it is "molecular chauvinism" to assume that
molecules are required at all; in a universe with different
properties, atomic nuclei or other structures might assemble in
totally unfamiliar ways.
If it is possible that sentient life does not necessarily have to be carbon-based, then how can we ever be sure what the real probabilities are for the observed values of the physical and cosmological constants?
We may never really know, since there may exist forms of "life" that is not even based on chemical bonds, but based on what we do know about chemistry and atomic bonds we can still make educated guesses. So while it is possible that non-carbon based life exists, scientists suggest that in order for life to come about using another element it must possess sufficient reorganizational complexity. This narrows it down to a lot fewer elements, and we know the quantities of these elements in various parts of the solar system, so from there were can make educated guesses about the probability of life occurring.
But yes, what you point out is exactly why the "Fine-tuned Universe" argument has never been very compelling...