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.
https://en.wikipedia.org/wiki/English_possessive#Nouns_and_n...
https://en.wikipedia.org/wiki/English_possessive#Nouns_and_n...
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://www.rit.edu/ntid/sea/processes/articles/grammatical/...