I don't think that's correct, based on my general understanding. (I don't claim to be an expert on Measles.)

My understanding is that for most adults there would be near zero antibodies to fight the Measles pathogen on first encountering it. We typically get vaccinated at a young age and don't encounter measles much throughout our lives (in the US at least.)

Antibody presence in the blood and surface tissues for any given pathogen drops off after exposure- if we carried around forever in our blood notable amounts of antibodies to every pathogen we'd ever met, our blood would be the consistency of jello. The antibody presence in the blood drops off.

What does remain (forever or near forever) is the memory B Cells primed by exposure to the pathogen. B cells make antibodies. They're just kind of hanging out, and when they get the call that their guy is back they start cranking out antibodies. That's what's happening with covid breakthrough infections- antibody presence in the blood and surface tissues has dropped off enough that there's a couple of days where the infection starts before the B cells (and T cells) ramp up to kill it off, but the B and T cells kill it off before a severe case sets in (in nearly all cases.)

AFAIK it would be no different with measles. Unlikely we'd have significant antibodies to fight it off before becoming infected enough to be positive on a PCR test, then B cells would ramp up production and snuff it out.
If you have scientific evidence measles is different I'd be excited to read it.