> If he didn't know any women at work that he trusted with this then that itself is a huge problem.

Given the fact that he was fired over this, i.e. Google thinks it's very bad, and assuming he had a hunch this was so, is it reasonable to believe he should be able to trust a female coworker with this memo not to file a complaint?

Put more generally: is it reasonable that one should expect one's coworkers to keep silent about a fireable offense?