It’s not untrue. It has been demonstrated in dozens of reviews that the M1 Air throttles under heavy load. Just because it hasn’t done so for your workload, doesn’t mean it isn’t happening for others.
Besides, when it throttles, it’s not a huge slowdown, so most people wouldn’t notice it “skipping a beat” anyway.
There is no perfect solution but I think annoying some users by sending them an additional email to confirm what you are doing is preferable to annoying some other users by taking actions without informing them. Honesty really is the best policy.
But it's much worse for the operator of the list to take actions which are invisible to the user. That's why I agree with mcv's point here. There is no perfect solution, someone will always be unhappy, but I think it's preferable to send an additional email to your user explaining "if you don't do X, then we will do Y".
They may well consider this email to be an annoyance, but I think that's better than making an assumption, taking an action and leaving users in the dark. Some will prefer that, but some will be confused about why your service isn't working for them.