I don't know if the snail in question is actually a nerite or not. it is the one in the first photo in this thread https://forums.thinkfish.co.uk/gallery-showcase/snail-photos/I recognise that possibly-nerite's colouring from being similar to https://www.pro-shrimp.co.uk/snails/1558-horned-nerite-snail-sun-clithon-corona.html. My nerite spends time in the location you and Sue describe - but I don't know whether or not he eats the algae, for the same reasons as Sue mentions.
@fcmf have you ever had problems with having to "rescue" Nerites after they've fallen over...?