How could any tower ever issue a "clear for a low approach" (whatever a low approach might be, I never of such a beast?) to a plane on final? Wasn't I taught final is where the approach ends and the landing begins?
I think it comes about for instrument training flights as we give a discount on the fees if they don't touch the runway. I presume this is similar at other airports.
We normally clear (instrument) training aircraft for a low approach and go around (without any restrictions) and the results can be quite different. People on initial instrument sorties normally go around from their minima, but the military jet trainers often get almost all the way down to the tarmac (maybe only ten feet above). I suppose it depends a bit on how brave you are!
Sorry to talk like being stupid and/or a foreigner - I certainly feel like both!
No need to apologise!