Ouch. My takeaway is that I should probably delete my slack account before leaving the company.
They're different parts of speech from the same root word, after all.
The word "private" means "having privacy" in the normal, everyday sense. Using that word to describe something that isn't private is lying. You and I both know there do exist many people who suffered consequences for not understanding the definition of that word.
In my opinion, the ethical thing to do is to use a different word when no expectation of privacy applies. And the upside is powerful: transparency gains trust.
Slack did this well: they call them "direct messages".
If you need privacy, use your personal phone (and don't connect it to the company wifi)