I worry about this risk a lot. There is no way to delete DMs on Twitter; even if you delete them they stay in the system so the other side of the conversation has them. To folks below saying "that was always true", yes, but I trusted the previous management of Twitter to not snoop on my private DMs. I do not trust the current owner the same way.
(I had a typo in my original comment btw; I said "surprising" but meant "unsurprising".)