How much lower, in the case of explicitly private information? I mean, the contents of the e-mail in the made-up e-mail scenario are no less of a lie than “I won't tell anybody” before asking in the truthful e-mail scenario.

It's a fair question. It's tricky for me to answer as I'm using my black box of social intuition to guess how people's minds would work in a (relatively) uncommon situation I (thankfully) haven't experienced, and it's hard for me to open the box to see what model or evidence my gut's calling on. I guess a kind of situation I have in mind is someone who says "I won't tell anybody" with fully sincere intentions when they say it, but conveniently forgets about that before/at the time they start disliking the disclosee. I don't know how realistic that scenario is, though.