Sounds like she's cracked. My DS couldn't say any more than about 10 words at 2 years old. Now he never (affectionately said of course!) shuts up!
Every child is different, and that doesn't make you a bad mum. As for TV, kids learn from EVERYthing. It doesn't hurt them to have a little educational background noise as they go through their day, I used to leave it on when DS was little for that very reason. It wasn't his focus, but it was there to jog his memory every now and then.
I used to play Playschool cds for the same reason, so that he could learn nursery rhymes, abcs and numbers without me having to feel like a broken record constantly singing them.
There's no substitute for good parenting, but I don't see how having the telly on in the background while you're getting them ready etc. in the morning makes you a BAD parent!
I don't think you should feel bad at all. Some nurses just feel like they have to make you feel bad or they aren't doing their job! Sounds like she was one of them.