Muntz,
Looks like you are outvoted.
Notwithstanding flying training is aerial work, owners of an aircraft have always been able to have training and checking in their own aircraft.
Indeed, I can thinks of a number of instances where those who are conducting training and checking do not have such an aircraft "on line", the only aircraft available is the owner's personal aircraft.
Think various SA226, AC690-695-G1000, B90/200/250/350 etc.
Tootle pip!!