An AI can't do any job that requires a body, so clearly that isn't true.

If you mean mental jobs, this could be true in the future, but right now, it's hard to say. You can imagine scenarios where an AI does 95% of a job but a human is still required for the last 5% (without which the first 95% is useless).

These tools are recent, but not THAT recent. GPT3 is nearly 4 years old, Copilot is 2 years old, ChatGPT is a year old, GPT4 is 8 months old. No large-scale employment changes resulting from AI are visible so far.

My guess is that some people will always be stubborn and prefer me over an AI giving them massages every now and then, even if I won't do them as perfectly.

But at that point in time, I think me giving one massage would perhaps be enough for me to retire for life, as long as I can abstain from buying luxury goods or services, i.e. those provided manually by other people (instead of AIs, whose labor would be practically free).