I used the wrong term, I meant tire slip. But you're wrong. You don't need bad tires, and you certainly don't need to "stand on" the brakes to activate ABS, you just need to exceed available traction enough that the speed sensors detect slip. I had Pilot Sport 4S, with less than 1000 street miles on them, and I used a lot less than 50% brake pressure in that turn. They worked perfectly after they were up to temperature and at lower pressure.
Have you braked in a corner at 120mph? It's kind of an edge case for most drivers not on the autobahn or a racetrack with high speed corners. Common sense doesn't have anything to do with it, clearly, because I just gave you another anecdote that shows the ABS can and did come on in a similar situation, and should have (in mine). But I'm just some guy on the internet, just like you and the OP.
OP- you might try braking a bit before entering bends at that speed, to bring the tire temp up a bit and see if that helps.