In our massage school we have had a 17-year-old student; until her 18th birthday the school would not allow any of the male students to be her practice partner, even right there in the classroom - presumably because under the sheet she was stripped down to underwear. It's too bad that touch and nudity aren't socially well-defined enough to be permissible with all ages. But they aren't, and they're not; in a touch-deprived, body-negative society they're too charged with need, and all too likely to lead to real disruption and exploitation.
I agree that it is a shame that our society has created a "dirty" mentality about nakedness and touch. I was an instructor at a massage school for a while, practiced at a large spa for a number of years, and have been involved in massage and bodywork either professionally or as a hobby for most of my life, and I have seen the entire spectrum of response/reaction to nudity and touch. I have had clients who were minors, and there were very specific protocols in place for that, and I have had discussions with other therapists, clients, and instructors about similar situations.
As for the Skype request -- I agree that it is just too big a risk. I know families who are nudist/naturist with their children, I have known people who grew up in nudist families, and I am happy to visit and spend time hanging out with children/minors in social settings with their families, but in person or online it is too much of a risk to even associate or communicate with them. I hope that my sons (ages 2 and a half, and 7 moths) will grow up with a healthy attitude towards the human body and nudity and human touch; I want them to enjoy the life that they have in the gift of their bodies and always appreciate the miracle of life and the love of humanity, and I hope I can instill in them the respect and common courtesies to be responsible young men in how they treat themselves and others. Our society has sexualized everything, and oversexualized most things. Sex is natural and should be appreciated and enjoyed when appropriate, but should also not be the sole purpose of existence. But I digress... sermon at 11 on Sunday. LOL