Depends on 'what' is doing the supporting. That is my first response to this. For a well supported spiritual idea (i.e. that spirit is found within consciousness) is not likely to become a fact in the materialism scientific sense.
Second response is that from both Wikipedia explanation on scientific theory and my own understandings, it is tangential to contextual facts. And as Wikipedia states, it is the abstraction of observable phenomena ... that leads to philosophical construction that the data in a theory is based on fact.
So, a well supported theory is one that has verifiable observations. But, IMO, here is where things get a tad hazy (just a tad) while leap in logic is made. It must be not just testable, but reproducible many times over, and this is what is equal to 'well supported.' The explanation of empirical phenomenon I believe (strongly) is tagged on after the fact. I realize it is there at onset, as method to some degree demands it, but the conviction that the phenomenon is empirical is done in formulating the theory. As Wikipedia states... "A scientific theory is constructed to conform to available empirical data about such observations."
Thus scientific fact is assigned when the empirical data is such that there is confidence that all observers who conform to the (understanding of the) reproducible experiment, will encounter same, or rather very similar, phenomenon. Scientific fact is a contextual reference within framework that is scientific method. Outside of the paradigm that is (materialistic) science and method, the phenomena may or may not exist as objectively factual.