There are degree-conferring post-secondary schools like VTC, which are not "universities". So may be our friend is such a student. The traditional university institution is transforming and he may loosely be considered a university student. Who is to quibble other than employers?
I've lived and worked in the UK and went to SCHOOL at one of their "universities" and I find myself slowly being driven insane by UK English. The worst is when an American starts doing a Madonna. Had a colleague from OHIO state that a client had "thrown a wobbly."
I take great pride fighting a determined rearguard action against "whilst." What are you, a 19th-century Cockney bootblack?
"Please guvna, hold me brush WHILST I gets in me chimbney, I does."
In American English you can use the term "school" for anything up to and including university. They are just different levels of schools. My university consisted of several colleges and schools, including the School of Medicine, School of Education, etc.
In British English school always means primary/secondary.
In HK people pick up different English influences depending on what school they attend, where their parents are from or studied, etc so being pedantic about this on Geoexpat is kind of obnoxious.
Neither usage is right or wrong just different. Non Brits telling Brits what they say in the UK is weird though.
I lived in the UK 10 years and it drove me crazy that people would act like they can't understand Americanisms when if they thought about it for 5 seconds they'd understand. It's snobbery. For example, pointing at dark red vegetable saying "beets." Response "WHAT?! WHICH ONE? BEETS? WHAT IS THAT?"