Like @bdsa points out with their example, the singular and plural are actually spelled differently, viz. "parent's house" and "parents' house", despite being pronounced the same way.
Oh that's interesting, thanks! Not a native speaker but I dimly remember hearing about this in english class, thanks for reminding.
I guess then the PhD student is indeed grammatically a singular then. It can still refer to a PhD student in general though instead of a particular one.
https://en.wikipedia.org/wiki/English_possessive#Nouns_and_n...