That's actually why lactose intolerant is such an interesting concept it doesn't really work like that, I've known plenty of lactose intolerant people who eat milk products here and there and then their kids even you don't get over it really.

There is no activation of the gene because it's not turned off in the first place the gene has your stomach produce an extra enzyme when you don't have teeth to allow the mother to concentrate nutrition for you.

We are not the only mammals with that gene the difference in someone who is lactose tolerant so to speak is it's broken.

It never shuts off even after it's actually a burden on the body if you weren't consuming milk, furthermore milk between species is far from a perfect exchange the reason we need baby formula instead of just giving them cow's milk is they would become malnourished.

The nutritional mix is calibrated to the animal the kids would have to be older in which case they would likely have lost their tolerance it drops off extremely quickly.(and drops off even if you drink milk.)

So as your article said it would have had to have been adults that drank it well feeling sick over and over and again the cheese idea means someone was already drinking it.