There is nothing to stop a female from swimming if she uses a tampon. As far as being unsanitary if some menstrual fluid gets in the water, it is no more unsanitary than sweat. I think I have read that blood is bacteria free. Given how sensitive young girls are around issues of their period, I think I wouldn't have said anything to her about it or kept her from swimming.
it's rather beneficial of course to wear tampon rather than pads when you swim. the trick is that you should not allow to stay wearing tampon of more than 6 hrs.
I also swim a lot and I swim whenever I feel like it even if I'm having my period or not..and praise God, there's nothing wrong with my reproductive health..until now, I'm very much fine and always in best of health.
there's what they call menstrual cup that should be insert in vagina which is more hygienic and safer than wearing tampons. it can be actually worn for less than 12 hours.