I've found the dumbest "fact" ever mentioned on memory alpha

[DevilEyes]

^ I suppose that was meant as "I agree with her".

A science academy for the whole planet, or a university for an entire state, is easier to swallow than a university for the whole planet.

No.

I love eloquent responses!

 

[Pavonis]

A public university is just a university supported by public funds, usually provided by a government. If Betazed is a politically unified planet (it must be if it is a Federation member), then the government of Betazed could support a public university called the University of Betazed.

Alternatively, the University of Betazed could be the administrative umbrella under which all universities on Betazed have fallen over time.

Another possibility is that the University of Betazed is a small private liberal arts college with a pompous name to inflate its importance in Betazoid culture.