Actually, in philosophy of science, falsifiability has been dead for decades, thanks to the Quine-Duhem Thesis. The Quine-Duhem Thesis states that a theory never makes a prediction in isolation, but does so in conjunction with auxiliary hypotheses and propositions about initial conditions. This means that when we are faced with an observation that apparently falsifies our theory, we always have the option of "explaining away" the observation by rejecting at least one of our auxiliary hypotheses or propositions about initial conditions. (This does lead to the theory becoming more ad hoc.)
Falsifiability has pretty much been replaced by Bayesianism. Bayesianism uses Bayes' Theorem (used in many spam filters, btw), and allows us to talk about an observation confirming or disconfirming a theory. Confirmation does not mean "prove," it only means "makes more likely to be true." Same thing with disconfirmation: "makes less likely to be true," not "falsifies." This is a better fit with actual scientific practice, since scientists tend to look for evidence that confirms their theory, not evidence that fails to falsify it. But for some odd reason, philosophically aware scientists haven't gotten the memo about all of this, and they are still talking about an account of theory confirmation that's been dead for about 50 years.
Philosophers also think that you are never required to accept the results of a non-deductive argument (including the results of abduction, aka the scientific method), and you always have the option of withholding judgment. However, if you do accept a well-confirmed theory as being true, most epistemologists (who study knowledge) would agree that you are justified.