It simply does not require a change in genes to stop teeth from growing. DNA methylation, which does not itself change the genome ~ not even to transpose a basepair ~ can do the trick all by itself.
That's fine, but why and how did the methylation change in actual birds? Are you saying it was not due to some other change in the DNA? I'm not talking about what goes on in the lab, but what went on in the wild.
But in any case, all this is beside the point. Darwinism (and indeed evolution) isn't tied to genetics, obviously: Darwin knew nothing of genetics. All that is required is an inherited change. As you say, all birds expressed teeth at one time. As you know, no birds express teeth today (except under extremely special conditions). That's an inherited change (genetic or not). Evolution by definition.
One process for suppressing a gene is called "DNA methylation". There may well be others, e.g. a demiurge from the quantum processor in each cell ~ something like that ~ we just don't know yet.
No change in the genome is required for birds to NOT express teeth, nor is a change in the genome required for birds to express teeth.
Mammals somehow suppress the growth of extra tooth sets ~ reptiles have no such problem. Neither do birds. There's work afoot to determine how we can remove the suppression ~ and thereby eliminate dentistry.