I guess it is technically true that they would be okay if it turned out determinism was false, since their argument is that determinism and free will CAN be true at the same time. Their line of argument is only really worthwhilein the first place if you believe it plausible that causal determinism holds. And I think most of them do (maybe it's telling that the position is also sometimes called 'soft determinism'). If they denied determinism from the outset, they'd probably be in the 'libertarianist' camp instead (not to be confused with political libertarianism).
The 'tree' of positions relating to determinism & free will is roughly: Do you believe determinism and free will to be mutually exclusive? If no: you're a compatibilist. If yes: you're an incompatibilist. -> In which case: do you believe determinism to be true OR do you believe free will to exist? You believe determinism is true: you are skeptical about free will, to you free will is an illusion. You believe free will to exist: You're a libertarianist and believe complete determinism not to be true.
Although often much lengthier and more technical than Wikipedia, the Stanford Encyclopedia of Philosophy has very well-vetted entries on philosophical topics, where the authors all are scholars in the respective topic and are asked to write introductory entries (potential downsides: English only and not always completely novice-friendly). There is one on compatibilism, too https://plato.stanford.edu/entries/compatibilism/