True or False?

False, the more resolving and balanced the system is the more sensitive to tweaks whatever that would include, cabling, room treatment, fuses, power distributors, ac receptacles, vibration control.
As for manufacturers, they are not  denying anything for a simple reason that all use better cabling and better means of support to evaluate or demo.

We all can agree that even the best speakers respond to room placement but is it true or not true in (your experiences) that the better your audio components are, the less they respond to various tweaks?

I would hope that we all can agree that ALL speakers respond to room placement. This is after all physics. You would at this point have to find another universe for this not to be the case.

These smoking room hypothetical word games are kind of blasé so let me just say no, it is not true that the better gear does not respond as well to tweaks. Not at all. No way. Game over.

@mapman

The better they are the less tweaks needed to make them sound good. See how that works?

There is a certain amount of truth there. Yes, the better equipment does sound better. That's why we use the word "better" to describe them. But the question posed was about the better equip responding better, not "needed" as much as we think of our systems, they are not a need. I have found joy in listening to music on the most basic of machines. Do I "need" the better equipment? No. But I prefer it. If you prefer not to tweak, that’s fine with me. It’s your system to do as you please with.

The better the system is the easier it is to make it sound worse. When you are at the top of the mountain the only way forward is down.
Tweaks are for idol worshipers. If it works, it is not a tweak but rather an essential accessory.