But being caught in a lie would destroy your clout instantly. If they're competing for clout there would be a big incentive to prove the competition wrong.
There is something to that, in that money gained will be kept (unless lawsuits can claw it away for fraud), but with both scenarios the ethically lacking individual would still have enjoyed the time until they were caught and future money/clout would both be hampered.
As for competition, that sounds the same to me. There is already competition for positions and grants, etc.
I mean, science doesn't pay for itself. You need libraries, you need universities, you need equipment. Only a mathematician can get by with a $5 black board and stack of chalk, and even then not very well.