Posts deleted by moderators aren't "deleted"

[Meirion]

Well why does it matter if they know about the bin or not? What is it to them?
I think this is a very good idea.

Tell them it for your own saftey just so you have records of posts for legal reasons or something like that, say in case of any disputes.

With a bit of fiddling on the moderator "delete/move" teplate I'm you could change the delete radio button and put in another hidden form field (I'm pretty sure) to make it move to the recycle bin but still read "Delete post".