And thus likely checked over by a real human? That's a logical leap, I think. I can easily imagine passing private messages through a Bayesian filter to catch

And thus likely checked over by a real human? That's a logical leap, I think. I can easily imagine passing private messages through a Bayesian filter to catch "inappropriate" messages, without needing human intervention. But, yes, if you are using a third-party service to communicate in plain-text, there is no such thing as "private."