Maybe it would help to see similar examples where THAT is used to connect:
She's the best friend THAT I ever had.
It was the worst movie THAT I saw last year.
I think what makes your example confusing is that it's dealing with a comparison, which makes it seems like it should use THAN. But for THAN to be correct it would be something like:
The number of students now at university is higher than it has ever been.
Also, comparatives (more, higher better) use THAN, but not superlatives (most, highest best).
Hope that was helpful.