[Palmer]

If a monster doesn't ATTACK you (Amazon, Lawyers), then it is not combat.

If a monster does not PURSUE you, that IS combat.
Running away is what happens when you lose combat. The monster not pursuing is simply a modifier on that step. Combat still happens - fighting is a separate step from running away.

There's a BIG difference between "Won't Attack" (which also means you can't kill it) and "Won't Pursue" (you can still fight it and win, you just won't get bad stuff from losing)

Stoned Golem: If you choose to just walk past it, it is not combat. That falls under not attacking.