I'm as certain as I could be without having met your daughter that it will be the fashion/peer thing that is motivating her. I suppose there could be an element of the rebellion/shock-the-parents thing, but, well, that kinda is fashionable when you're sixteen.
Personally, I don't see a problem with a girl of that age having a belly button piercing - she's the one that's going to have to pay for it (unless you're a softy), keep it clean, deal with it if it did get infected, etc. - but she's your and Silver's daughter so it's your and Silver's decision whether to let her do it or make her wait another year.
Drink coffee and do stupid things faster with more energy.