Kids teeth have nothing to do with whether they drip from cups, bottles, or a gallon jug. Holding the bottle in their mouth all night with milk dripping on the teeth however does. Your child is just a victim of bad genetics like the dentist said. I would have kept looking because most Pediatric Dentists are now using white fillings and caps instead of the silver. Our Pediatric dentist is in practice in a clinic with several other docs and he uses only white material for baby teeth. he understands how cruel kids can be and has never used the silver. Most of the time it is older docs who won't use anything but silver.
Anyway, as you know this is just the start of a life of dental visits and fillings and caps. I have weak enamel and have missing teeth now because my teeth just gave out, they are so bad I can't even get them filled. You need to make sure you are an advocate for your child. Don't let them put more silver in there, find a Pediatric Dentist who only uses white material.
You did the best you could and this is not your fault. It is a genetic thing. If having a drink around all the time was as bad as some moms would make you think then every adult would have tooth rot from excessive pop drinking and too much other stuff in their mouth all the time. Saliva washes/rinses the mouth out all the time.
Good luck with your child's teeth, chances are these teeth will be gone by the time he enters school, or at least 1st grade, most kids start loosing their baby teeth at 4-6 years old.