I'm a dentist with over twenty years experience in general practice.
I've seen this happen only once in all those years, so it is extremely rare. In that isolated case, it was a combination of several factors- already weakened, hypomineralised enamel, the fact that breast milk contains more sugar than cows milk, extended feeding, and not brushing teeth after the feed.
But it is extremely unlikely, so I suspect there was another contributing factor such as hidden sugars, lack of fluoride perhaps...
For those posters saying to OP to get a second opinion, the OP will have already received it. Once decay is noted in a child, and if deemed unsuitable for treatment in general practice( due to young age or pre-cooperation), the dentist automatically refers the child to a hospital setting.
The child will be examined by a consultant first and foremost, who, after discussion with parents and other health professionals, will decide the best course of action. In this case, GA, and surgery to remove the teeth.
It's not a decision that is taken lightly, and there are strict guidelines to follow.
At any rate, discussing whether the dentist was right or wrong is not helping the OP. I think your wee one will be fine. Children are very resilient. Your child will be offered analgesics. Plenty of cuddles.
I would insist on some follow up appointments in order to determine the root cause, and how to prevent further deterioration.