You should talk to your sensei to find out exactly why he only wants his students to stay within the org. I can think of the problems arising from using different verbiage to the sensei having troubles keeping everyone on the same page during practice. It is also possible that he wants to keep his style of aikido pure to its origins ala Saito sensei.
I train in another art as well as self study in other aikido styles from videos and youtube. It can slip into your practice while on the mat.
I dont see that talk going very well. lol. I do see my Sensei wanting to transmit his teaching of his teacher purely to his students. But there is so much out there, isnt there much more to learn than this senior Shihan's style? Its not as if I am refusing to learn his style but I would like to learn more from others as much as possible.