A Picture In Picture "result" can be brought about at either Track Level or Event Level. It's your call.
It was my understanding, and I may be incorrect, that Ulf was concerned about only this particular Event ("clip"), viz:-
"I know I can take the clip full size, make border and render, import and then scale and rotate it, but the other thing would be much easier."
Consequently I surmised that Ulf had wanted an outcome only to the Event. That is why I made my references to Events, but you/we could do the same for a Timeline. However, that WOULD mean having a Border Fx running the whole length of that Track. Unless I need to, I don't this.