Both of these positions are valid objections. The FBO or the airport
authority or whoever or whatever is responsible to the insurance company
covering liability for the airport not only has an inherent right, but a
responsibility to insure that anyone conducting a business operating
from the property has been duly cleared to do so by the insurance
covering the airport.

Doesn't make much sense to me, does this also mean that a CFI
operating out of another airport cannot come to this particular
airport and give instruction in the pattern for example? A CFI could
easily fly into this airport with a student and give dual instruction
from scratch. Would that be banned also? Would this airport also ban a
student from flying solo into this airport for liability reasons? Any
number of unknown people can fly in and taxi around the airport every
day and to pick on flight instruction for "liability reasons" which is
also supposedly the safest form of flying activity is bizarre.