Do mods actually have the power to deprive the user of the usual notification by PM?
Yes.
ON another SMF forum there is a post:

As a global moderator I click delete and get this dialogue box:

I click ok, and the message is gone.
No advice to the user.
Which is why I know the moderators are making bold face lies about what they can and can't do here. It only takes minutes to set up an SMF forum on a website (and it's free!) - give it a go and see what you can and can't do Vs what you are told can and can't be done on an SMF based forum.
So where exactly is the
deprive this user of notification box or button? The only person that is lying here is you. You're spreading misinformation about something you know nothing about. Again, you really don't know how this forum works. Stop being paranoid and stop spreading false information. Do you really think I'm going to publicly post a 'bold faced lie' when theymos or any other mod could contradict me or prove otherwise? To reiterate a
fact: staff here cannot choose to deprive a user of a notification of a deleted post. Whether you can on any other version of the software or on any other fourms is irrelevant.