There are two parts to the issue: a) the general "intellectual" (or "enlightened" or "educated" or "liberal") population's belief in scientific theories and facts: while some atomic premises in science may be unexplainable, higher order claims are (that after all is what makes science interesting!). But people believe in some claim or other simply because it is "scientific" (as I mentioned elsewhere, some of this due to pragmatic shortcuts). For instance, one can explain the chemical bonding (say ionic) by just stating as "fact" that elements tend towards their closest noble gas (or some such) or explain it further using Pauli's principle, or dig a bit deeper into the reasoning behind the principle... b) your more general question on the basis of scientific laws and facts. I think you are quite right in your characterisation. But then again, anyone can make generalisations from observations. What makes science different, if at all, is (a) either claims to theoretical explanation -- deduction (discussed briefly above) or (b) parsimony. But sometimes that parsimony is a luxury and is at a cost.
Which throws me back into the "science vs the rest" debate. So, let me bring it back to the issue at hand, of faith: what my scientific education taught me (unintentionally) is the treacherous nature of the faith that one nonetheless needs in order to be able to say or do anything at all. In that sense, it converted me to atheism, by which I mean a wariness of absolutes. ;-) (some would call that mere agnosticism, which I am willing to live with).
--ravi