Does "could" always mean something less likely than "can", even in backshifted subordinate clauses?

Solution 1:

Could is not always less likely than can. Nor is it more likely. It isn't always anything; it's not that simple. In all of the above examples, it can (or, if you prefer, could) indicate less likelihood; but it can (or could) also indicate something different (like a different set of assumptions to draw conclusions from); and it can (or could) be pretty much indistinguishable from can.

A great deal depends on individual usage. People form habits about how and when they use which auxiliaries. In particular how they pronounce them -- intonation matters a lot with modals. Consider the many many ways the following sentence can be pronounced, including suppose and could (not to mention Well,):

• Well, I suppose he could do that.

One can vary from certain affirmation to vehement denial, depending.

The big mistake is supposing that modals have fixed, simple meanings, like nouns. Auxiliaries are part of the machinery, and modals are far more complex than most engines. Modals are about variability, statistics, and individual judgements. They always represent somebody's judgement, but whose, and how good it is vary considerably.