I really really really do not trust companies on the verge of IPOing from goosing their numbers. Even if the lawyers are up their ass, the social pressures are more than enough to compel the behavior. For every good person willing to do the right thing even at the cost of a delayed career progression, there are 20 people willing to do anything not even for a dollar but for an "atta boy!" from the boss.
The most plausible approach would be for Anthropic to train some separate classifiers to detect benchmarks. I'm not saying it's completely impossible but IMO this is conspiracy theory levels of effort.
You're absolutely right that it is a game of whack-a-mole and eventually we may have leading private + credible + popular benchmarks that ultimately dissuade the behavior, if it can be dissuaded.