I see this on threads and posts all the time. People saying that they don’t want this appearing in the tabloids so they don’t give permission.
Thing is, as much as I despise the Daily Mail and its ilk, the reality is that as soon as you write and publish a post on MN that post becomes the property of MN, and you lose all right to say what happens to it.
Added to which, you’re posting on a public platform, so again, you have no idea who is sharing it and where and when and to who else.
If people are that afraid of their posts appearing in the DM, then the starting point is probably to not post on a public platform.