Absolutely. But if you have the choice between a) not knowing 100 pct of the time, and b) knowing for certain it's not private X pct of the time, for unknown X

Absolutely. But if you have the choice between a) not knowing 100 pct of the time, and b) knowing for certain it's not private X pct of the time, for unknown X probably not 0, you'd want b. You will have more information by trying.