I am doing C1 training at unit and at my parent unit (got to love the RTC system), but someone is potentially trying to stop it, especially with my parent unit. Even though none of the training is dangerous,
it just seems like a cnut does not like "attached personnel" getting ahead or doing other things.
Why do C1 training anyway? If you start doing it for free they'll start expecting everyone to do it for free, you should know what a bunch of penny pinching and vindictive cnuts the MoD can be when they set their minds to it.
And the answer to you question. While you are on his/her books, the authority for other training lies with them. I had to stop it for a number of soldiers who ended up doing far more training outside of the unit they were on strength of than in it.
The odd bit of training elsewhere (paid or C1) is fine - if it gets to be more than that then it is reasonable to be asked to concentrate on your own unit or seek a transfer to where you seem to want to spend your time.