You're right, and it is really frustrating, especially as it was working fine at first!
To make the footage editable in other programs (for you Premiere Pro, for me Vegas Pro) you need this:
It's another step which shouldn't be necessary, but at least it's simple and works fine.
I don't know what you mean that "...the files remain on your phone as data or cookies or whatever..."?
Deleted is deleted, right?
I'll certainly try deleting and re-installing the app, but I seem to remember already doing this, not sure now, I have tried so many things...!
Thanks for the help.