I'm with Mack...I would be reluctant to take a person I have never met, and don't know, out to an emergency call...
I know of many brigade who cross-crew....which is an excellent concept...I have some of my members who spend a fair bit of time in another brigade's area (and a long way from my brigade).
He asked about what did I think about him responding with that brigade...I told him he should - but he MUST make contact with the other brigade, and chat to them..so at least they know who he is, and can do some checks on him, should they need to....
There is an argument that everyone has done BFF-1 and is capable of responding....that may be true (but in some cases, may not..) but, that aside, at least if you go out with another brigade, they at least know who you are, BEFORE the s*%t hits the fan...!