Ah! A pet hate of mine! Long fingernails!
Long nails do get in the way of good piano technique, perhaps moreso for someone who is learning and not yet developed a good technique. The tips of the fingers need to be in contact with the keys and the pupil needs to learn to trust her sense of 'feel' on the keys. I often find students with long nails need to look down more because they physically can't feel their fingers touching the keys: the end of the nails are dead. Then of course, this leads to sight reading problems!
In a five-fingered position, for legato or staccato playing, the fingertips should be touching the keys. It's only when you start to stretch that the 'pads' of the fingers come into play more. When playing on the pads of your fingers, nails are not quite as intrusive.
When it comes to getting my students to cut their nails, I've learn not to beat around the bush. I'm not unkind, but I say outright, "Your nails are too long. They're getting in the way". I also write 'please cut your nails' on their lesson notes, so if it becomes an issue, we can look back and see how many times I've had to ask! For a younger child, I can mention it to the parents and explain how much it gets in the way. To be honest, if I had a decent rapport with the parents of your 12-year old, I wouldn't hestitate in mentioning it to them. The trick is not to ask, but to tell! Don't go on about it for ages. Be concise. These nails get in the way of your job, and the pupil/parent is paying you to do your job properly.
Of course, if a student just forgets to cut their nails for the occasional lesson, that's different and you have to let that go.
I inherited a 12 year old student who'd had pretty poor tuition up to Grade 3. She played with straight fingers, lifted her hands up all the time for no reason, and she couldn't sight read two adjacent notes without looking down. After about 6 months of long nails, and me asking her and mentioning it to her Mum (who understood and tried, but kept forgetting), she still turned up to say, 85% of lessons with long nails. So, in the end, I told her that if she arrived with long nails, I'd have to teach her theory for the lesson. She was behind on her theory anyway, and needed it to continue with her clarinet exams. I explained it frustrated me that she'd only be able to benefit form half of what I taught in piano and she finally realised how serious I was... everything's ok now!