I really can't see MLB manipulating the testing. The benefit of doing something underhanded is minimal compared to the disaster that would happen should they get caught doing it. How hypocritical would they look if they were "cheating" to stop cheating?
But image aside, all it would take is one leak or slip up and they'd be open to all kinds of lawsuits, any bargaining power with the MLBPA for the next negotiations and of course an insurmountable PR crisis involving human rights and racial profiling that would cost them advertisers, broadcasting partners and viewers from all over the world.
Well the same argument can be made about cops planting evidence, yet we have seen them do it on camera. Several similar examples, from politicians to people running ponzi schemes- despite the fact its not mathematically possible for one to continue for very long.
Most humans, almost always incorrectly, think they are smart enough to get away with it. So they often don't weigh the pros/cons as logically as you just did.
I very much doubt that anything humans do that is supposed to be random, is actually random. Whether that's drug testing, security checks, DUI checkpoints, etc.