I feel like the Toupee Fallacy is lurking around in this conversation. We know how many cover-ups are successful, and the ones we know about are nearly universally unsuccessful.
Panic tends to bias towards action.
Just because there are only two possible outcomes doesn't mean that they are equiprobable. Not all coin tosses use a "fair" coin.
The percentages the comment you're responding to provides aren't probabilities, but damage fractions; 50% isn't a 50/50 likelihood, but 50% damage of the 100% case.
Fair coin flips have 50/50 odds. If we say that you get $100 if it comes up heads, and $0 if it comes up tails, then the expectation value for the money you'd have afterwards is $50=0.5*$100 + 0.5*$0. If it was an unfair coin with 30% odds of coming up heads, then your expectation value is $30= 0.3*$100 + 0.7*$0. And so on. The fact that the outcomes are dollars or damage percentages is irrelevant to the calculation.
* Successful cover up (0% damage).
* Failed cover up (100% damage).
* Don't bother (100% damage).
So if doing nothing and failing to cover up lead to the same result, you might as well give a shot at successfully covering up. Whatcha got to lose?
It is assumed not bothering is 100% damage because the screw up is apparently bad enough to warrant attempting a cover up.
In terms of risk analysis, rationally considering a coverup is in the same ballpark as rationally considering shorting a stock, in the sense that making the wrong call can cost a whole bunch more.
Did you mean "we don't know"?
The Dalai Lama literally pulled down a six figure paycheck from the CIA, for example. The government was, is, and will continue to spy on you.
The difference is that if something is successfully covered up for 10-20-30 years, by the time the public finds out about it nobody really cares.