No, really: we have the same problem in software. Software developers under high pressure to move tickets will often resort to the minor fraud of converting unfinished features into bugs by marking them complete when they are not in fact complete. This is very similar to the minor fraud of an academic publishing an overstated / incorrect result to stay competitive with others doing the same. Often it's more efficient in both cases to just ignore the problem, which will generally self-correct with time. If not, we have to think about intervention -- but in software this story has played out a thousand times in a thousand organizations, so we know what intervention looks like.
Acceptance testing. That's the solution. Nobody likes it. Companies don't like to pay for the extra workers and developers don't like the added bureaucracy. But it works. Maybe it's time for some fraction of grant money to go to replication, and for replication to play a bigger role in gating the prestige indicators.