I don't even understand why they're so insistent. They're risking far more harm than they could ever prevent:

1) If they're so anxious about preserving trust and credibility wrt vaccines, don't make absolutist claims unless you can prove impossibility. Perfect proof isn't needed, but "I can't see how it could happen" isn't even close to that. The medical community has already made multiple such blunders. See, e.g., claims that SARS-CoV-2 couldn't possibly be transmissible by aerosol; claims which were based on generally accepted yet bad science. In fact, the community had already made that same blunder years earlier with Ebola: https://mbio.asm.org/content/6/2/e00137-15 Fool me once, shame on you, fool me twice... that's how you lose credibility forever.

2) More importantly, what does it matter if it happens on exceptionally rare occasion? Or even regularly for that matter? The disease does exactly that.

3) Also, they're lending credence to the anxi-vaxxer narrative by implicitly accepting the premise that anything that modifies your DNA is suspect. In defending mRNA vaccines they're effectively throwing many other types of vaccines under the bus.