I'm not sure exactly what constitiutes 'overtightening' - the difference between just tight enough to stop the lig and reed slipping when I'm wiggling the mouthpiece onto the cork and so tight I can't turn it any more without using pliers is only a fraction of a turn on my ordinary standard metal two screw ligature. I assume with the 'thumbscrew' syle ones there's a limit to how far you can go.
I've not got access to strain gauges to measure the pressure exerted on a mouthpiece by a ligature and I doubt there's much data in the annals of materials science on the long term effects of pressure on the dimensional stability of hard rubber., but my guess is that you'd have to apply serious amounts of force on a lig screws for decades to get any deformation of the table - most conventional ligs on HR mouthpieces are going to exert pressure fairly evenly around the circumference of the mouthpiece rather than just on the table alone.
HR is an archaic material that seems to be rarely used outside of the world of traditional saxophone and tobacco pipe mouthpieces - more modern polymers have superceded it elsewhere.
The warping of hard rubber may be a more complex issue than long term ligature pressure. To some extent all moulded and cast items have potential problems due to stresses that may have built up in the moulding process.
Hard rubber is moulded using a lot of heat and pressure and can sometimes be inconsistent, so I don't know to what extent it might warp anyway, if left alone in a darkened room. I doubt that any research data exists because HR hasn't generally been used for precision components apart from sax mouthpieces..
I'm not denying the observations of experts who work on mouthpieces for a living, but I am aware that cause and effect are tricky devils to pin down and it's in the nature of the material universe to be more complex than we'd like it to be.
The worst problem I ever had with tightening a ligature was due to the mouthpiece being too smooth....
when I bought a brand new Jody Jazz 'HR' alto mouthpiece, I dropped my lig and broke one of the screws, so went out and bought a new one, fitted the reed and in the process of putting the mouthpiece on the neck cork the lig slid off in my hand. I put it back on and tightened it until it wouldn't tighten any more and it still came off. I realised that both the inside surface of the lig and the outer surface of the mpc were too smooth to grip properly. I had to stick a piece of tape to the mpc for several months until the build up of dirt, corrosion and wear and tear gave it enough surface friction...