Core strength matters, but the perpetual shortening of muscle strands is understated. If you're just standing on two feet, strong core won't keep your hips from being tilted back involuntarily, ime. Not how I got rid of the problem.

if you're working your lower back during squats, your form is incorrect and you're risking injury. Your spine should be neutral throughout the movement - the lifting force comes primarily from your quads and glutes.

Er, it's part of the posterior chain and squats will always target the lower back to an extent, both high and low-bar. Squats were one of Arnold's favorite lower-back exercises. No way you walk away from heavy squats without feeling it there.

to be clear, I meant working as in bearing load - of course your lower back will be active in stabilising your spine through the movement, as will your core. So you're going to feel that, especially if you're keeping tight. But your lower back shouldn't be generating the force necessary to lift the weight.

OK, we agree

Yes, you should not good-morning the weight.

But if you are low-bar squatting, your back isn't going to be completely upright, and so keeping a significant weight at a angle requires muscular contraction. Your back is going to get worked.

Hell, even high-bar isn't completely upright, and even if it was, you'll get tension there.