I have signed the same sort of contract in the past (probably with the same company). I don't know the legality of that phrase within the contract. But as far as FTL, if the pilot in question is only instructor, then FTL are not applied. Again I don't know the legality of that either, but I believe that instruction is classed as aerial work rather than public transport, so FTL's are not applied.
I believe the reasoning behind it would be that the company is protecting its name should you have a mishap flying or even have anything to do with the flying of someone elses aircraft.
Perhaps the first step would be to have a word with the chief pilot before engaging the services of a lawyer.