You don’t have to push. That’s only to get the pushing reaction from the opponent if he isn’t pushing or isn’t pushing enough to get the momentum you want. I’ve thrown it with minimal push-back from my opponent, but I was muscling it and it wasn’t as pretty

If an actual attacker has that hold on you, they’re either going to be pushing or at least leaning to hold their ground. The only way they won’t is if they’re trying to just lock you up, hold you where you are, etc.; basically a non-aggressive hold, if that makes sense.
Using my extremely scientific data analysis, I’d say they’d push more than enough 99% of the time

Maybe not driving you back into a wall, but definitely pushing more than enough.
Alternatively you can pull your opponent, but that’s not optimal.