Legit reasons for not being allowed to train at another dojo?

You mistakenly assume cross training means you can just train in another school anytime you want. If we were to really examine the true spirit of cross training and the context in which it is used by martial artists, it assumes that the one who cross trains already has achieved a proficient level of skill and understanding of the basics of his base art. Meaning a 1st Degree Black belt in Karate who joins an Aikido class can be considered to be cross training, but a white belt in the same karate school joining an Aikido class would not. A white belt does not have the level of understanding and skill in one art enough to be able to compare, differentiate and appreciate the principles of both arts, so how can he be considered to be cross training? He's basically just learning two different skill sets at the same time, which as most would point out can hinder your progress in both arts. So I don't see anything wrong with your instructor prohibiting you from training in another school while you are still at novice or Kyu level.