Sure, a high level Goju-Ryu karateka can watch a video of another Goju-Ryu kata that he hasn't seen yet, and replicate it very well including the small details. This is because his experience in the system has conditioned him to the finer points of Goju-Ryu and he already has an understanding of the dynamics and principles of the system. The same would be true for any high level practitioner watching techniques from their system. Notice I clarified this by saying "high level practitioner." Someone with only a few years of experience, or even a Shodan or Nidan (and probably Sandan), needs to stay off the internet. I'd say about 4th Dan is when someone has enough understanding of their system to be able to watch a video and replicate what they see accurately, and without developing bad habits their instructor will hating them for.
However, by taking it upon yourself to visit another school without consulting your instructor first shows a lack of respect. I am the founder of my own system as well as the inheritor of another, and I still call up my sensei who's 1,000 miles away to ask if it's alright if I work out with certain people. Of course, he has never said no and has repeatedly told me to stop calling about it, but he'll have to deal with it because I will never do that out of respect for him and everything he has taught me.
The best advice I can give anyone who is continually seeking information is to ask your instructor. A good instructor will be honest enough to tell you whether or not that particular technique or kata is something they can teach you (and that doesn't mean right that second). A great instructor will direct you to someone who can show you if they can't. All school owners know other instructors, whether or not we like each other. Martial arts is a tight-knit community and we all know who teaches what in our area. As instructors, it is our responsibility to guide you on the best path that we know how for your benefit, not our ego or wallet.
So for example, if you're a karateka who wants to learn ground fighting, don't try watching videos online. Ask your instructor if it's alright if you cross trained. As long as you are not trying to learn two contradictory arts (Shotokan and Goju-Ryu, etc.) and are seeking information that is not available in your system, your instructor shouldn't have a problem with it. If they tell you that what you're seeking is part of the system, however, then you owe it to yourself and to your instructor to continue training and trust that when the time is right, you'll learn whatever it is you're seeking. Don't get frustrated and quit because they won't show you upon command. Martial arts is about perseverance, dedication and endurance, and there is a natural progression to your learning. Don't try skipping ahead to the front of the line, or you'll be very disappointed with the outcome.