I am not trying to pick a fight but do you really have knowledge of the fossil history of the mudskipper?
Not of the mudskipper(s) in particular, but I know these fish are Gobies, and I have a pretty strong recollection that Gobies don't appear rather late (for a major group of rayfin fish), I wanna say as late as the Eocene, and in any case long after the first amphibians.