I actually think this is tied to the whole belt issue. I envision 2 different training relationships at work; that of a visitor, who only experiments with another system, and that of the person who chooses to learn a different system. Each involves a very different mindset. The visitor can pick and choose; they simply have to "play along" for the few hours they spend with working with the new system. For example, say I were to attend a few judo classes, simply to develop better breakfalls and learn a throw or two. I'm not trying to learn judo; I'm getting a few pieces of judo and grafting them into my home system. But, if I decide that I want to learn judo, I have to start at the bottom, and learn their ways of doing things, and I have to accept their ways as long as I choose to train in judo. (An analogy might be made between ordering a la carte and ordering a dinner platter.) If I'm experimenting or visiting, I may wear my black belt. But if I'm studying the system -- I'll wear a white belt.
If you choose to train in a system, you accept that you have to do things their way, at least while you are training in it. You don't, no matter your rank, have the option to decide which part you'll accept and which you'll reject; you're training in the system and that means accepting the whole thing. Of course, this is just my opinion... But if you want to learn about or learn a particular technique from another system, rather than actually train in and learn the system -- then you can pick and choose. You can dump what you don't like.