"Two caveats. This only works for a table with equal legs, where the wobble is caused by an uneven floor. If the table has uneven legs, you probably need the folded napkin. Also, the floor can be bumpy but has to be free of steps"
Spherical cows rearing their ugly heads once again
It also requires a table with multiple legs, instead of a single pillar table (common outdoors). If the top->pillar->base connection chain has a weak point that's wobbly no amount of rotation or napkins will fix it.
Which is bullshit because tables in a public space are abused.
I think the proof forgets that legs A and C are locked in a struggle over being on the ground. There is no guarantee that C is still on the ground when A touches.
I've had a great deal of luck getting the table to wobble less by turning it, but have also met with infrequent success. And square tables are more constrained to orientation.
For decades, I have been well known among my colleagues, friends and family for rotating tables any time there’s even the slightest wobble, not giving up until the deed is done, and nearly always doing so successfully unless a leg is clearly missing its foot. Most of them tolerate it.