[RedDevil]

Argon is slightly (38%) heavier than air.
It will transfer more sound that air does; by that dampen the vibrations in the rubber.
A lighter gas would isolate sound better, but also dampen the vibrations less.

Even so argon is over 300 times less dense than rubber - and that's assuming 30 PSI in the tire. At such a low mass it can only seriously dampen harmonic vibrations over some time; not the kind you'd expect in a tire.

There are, as far as I can see, 2 ways in which tire noise manifests itself; outside through the air, and inside through the rim, axle and suspension into the bodywork.

Try as I might I cannot see how the gas in the tire inluences that.
So, if it does there is something happening that I'm not aware of. That is really exciting, I love to learn something new.

Tire noise is entirely testable, all tires have data on road noise.
If the fill medium has influence there should be noise data available.
If it doesn't I expect there will be tests proving that too.

So, where's the proof, one way or another?
I cannot find it. AFAIK there is no proof that it matters, nor that it does not. Either claim is unsupported. I just don't know, and think nobody really knows (proof based).
Prove me wrong on this - if you can

One thing - if it does matter, it would be interesting to know by how much it matters.
If argon would reduce road noise by 0.05% then it would matter, just not be worth it.