I am having a bit of difficulty following this since I do not use facebook.
First two general points "against" cross training.
1.) Students and teachers can wind up in awkward or even potentially hostile situations:
In an ideal world martial artists would exhibit fellowship, be polite to each other, etc. That is not always the case. Competition between schools is sometimes based on politics, personal issues and the like and can create genuine hostility. If sport "competition" is a goal game plans, strategy, training and coaching methods all sort of become a "secret recipe" in an us vs them situation.
So, teachers may be hesitant to have their students sharing secrets. Also, if the student winds up in a hostile school/gym they may be subjected to abuse. Now, maybe this is mostly a thing of the past, but it has resulted in very real injuries and feuds in the days gone by.
2.) The student may get confused.
This is one I agree with at least to a point. That point is about a year and a half of hard training past when the student thinks they are ready. Honestly, in the beginning stages of learning a skill different "looks"/teachers can sometimes do more harm than good. If the student does not have a decent handle on fundamentals than training with a bunch of different teachers/styles is often a bad thing. It is also huge drain as a teacher if the student is constantly asking "style vs style" questions. It can get ugly and loop back to point one if the answers the student gets are curt.
So, if the student is less than a year in, I really don't think cross training is as big a benefit. I will go so far as to say the typical white belt should eschew seminars and just get reps in on the basics. On the other hand, advanced students and instructors SHOULD be doing it. If only to pick up different ways of solving problems or teaching. Again, the typical black belt should be willing to miss a class in order to get to a seminar.
Now, I am not saying that either of these apply in your case. I am just offering up a "not all teachers who seem to discourage cross training/cross workouts among their students are wrong/bad" point of view.
In YOUR case I would ask for clarity face to face. It sounds like your Krav Maga teacher (the one that "sponsored" you) is toeing a hard line against "sport" for a reason. If you value him/respect him I would ask the reason. I would not ask it over a public media like face book. It could be a mis understanding between posts, or it could be "I used to let students do this until this other boxing/MMA/kickboxing gym got offended and barged onto my floor and challenged me. Nine stitches, mine, one bit off finger, his, and 20,000 in legal fees down the drain and it just ain't worth it."
If you respect and trust him I would give him an opportunity to answer your questions. You may be surprised. If nothing else I think it is the honorable thing to do.