That's a bit too simplistic -- if there is a small group that really pushes things forward in a big way, then maybe not, but if this result builds upon decades of prior work, then Cook and Levin might be equally or even slightly more famous than the solver group after the dust settles.

But it is a moot point anyway. Cook and Levin are very well known already in TCS, and credit is not directly enumerable like money, so "more than a lot of credit" doesn't make too much sense.

For this problem in particular, asking the right kind of question was really important for the field and led to a lot of discoveries even before it will be answered.