Their custom chips were not designed for "1.25GSa/s", sure. They targeted at least 2GSa/s. So they had/have issues with their design or/and technology, thus, imho, they do the binning.
Moreover I doubt the companies like Rigol (a rather small company) might afford itself the selecting of an already populated board like "pass/fail(trashed)".
Anyhow, yes, a higher BW needs a different settings of the AFE and its noise and drift will most probably increase..