Disagree that that implication follows as a rule.
While I agree that, in ideal conditions, bigger brakes don't stop a car beyond what the tire's friction can provide, there are plenty of cases where it's not so black and white or ideal .. heat dissipation being one of those cases .. even driving in rain can be one be an example like ability to shed water off the rotor.
I'm just saying what you said is just a bit simplistic ... and since I keep reading it 'everywhere' it seems more info might be more useful.
But it really
is black and white. It's pretty basic physics.
Bigger brakes
can not stop a car any shorter than stock brakes can, if both can engage ABS. Which again every production car I'm aware of going back at least a decade or two can do.
Even in the rain.
GRM Pulp Friction
Author teaches SAE master classes on braking systems, has written books on the topic, and has designed braking systems for racing teams, vehicle OEMs, and brake OEMs (like Stoptech). He explains what each part of the braking system can, and can't do for you.
And why the tires not the brakes are what stops the car.
If you need more sources I can quote you Brembo, Stoptech, Road and Track, even the folks who nationally test police car equipment, all making the exact same point... upgrading your brakes can't reduce your stopping distance, because physics.
Sticker tires are the only way to do that.
Changing your brakes CAN do many OTHER things (the link I provide describes them for each part of the system)....
one of them includes
maintaining the same stopping distance over many repeated hard stops without giving the system a chance to cool... which might be what you are thinking of.... but the car will still never stop shorter than it did the first time on stock brakes.... and the need for resisting brake fade we're talking about is mainly a race track thing and doesn't really exist in normal street driving unless you're involved in the chase scene from a Jason Bourne movie... (especially on a car with regen braking)