I expected you could offer better reference than that. I don't have time to study multiple hours of racing just to check a little doubt. Not only that, I don't think that reliable observations could be made this way. What should I do ? Watch and estimate how many times and how hard cetain car understeer and oversteer, and then make a graph ? Would it even really answer anything, since any good driver is a major influence if car gets pushed more to oversteer or understeer ?
I hoped you could offer some more precise reference, as you said that phenomenon is "widely known". To check this more reliably one should try it himself IRL, and do it without confirmation bias, and to avoid any placebo. Also helpful would be to find literal evidence by drivers or engineers.
For now, I'll stand by my thinking that mechanical grip balance should remain the same at any dry surface grip levels.
The only mechanical reason I could think of is that higher friction would aid to more body roll, higher centripetal accelerations. So I suppose whichever end experiences more load sensitivity (higher load switch magnitude), could have more impact due to higher cornering forces.
I have observed many times in different levels of motorsport this known phenomenon. One that comes to mind is Jensen Button discussing how that in early test session upon arrival at a new circuit that the team is constantly looking to solve oversteer but as the sessions progress the balance just comes back to them.
To help your understanding I even did some google searches and was surprised to see so few references but there were several in karting forums advising to "loosen up" the setup if the track is well rubbered.
I have experienced it IRL as a driver first hand when a test day on Friday yields some oversteer but by Sunday the car is neutral.
Rockingham was low grip and green, all teams needed to change car balance from higher grip track settings.
One very convincing item is that when F1 teams pit to change from a soft tyre to a harder tyre they reduce front wing to match the rear grip. (the harder tyre being a good surrogate for a less grippy surface). Total grip is reduced and the rear suffers more therefore the front grip has to be lowered.
In sim racing we do this also.
Last night in an FSR test race my first soft tyre stint produced even tyre wear, my second stint with same tyre , same fuel load the front tyres slid and wore more (I will screen shot the motec graph). This was due to increased track grip impacting the cars balance.
None of these examples involve the variables that you mention such as differing driver styles.
If you remain unconvinced I suggest you set up a test session at say Nazareth oval. Set realroad at green and progression to a to a multiple. Start the session with a good car balance on the green track and drive. Keep putting on fresh tyres. You will find the car becomes more understeery as the grip improves.
Beyond that I cant make it my career to convince you of this phenomena.