Sure, that was one post in the thread. Gotta read the whole thing (or more than just the first post) to get the real story. Otherwise misinformation is spread yet again.
And while I certainly could be wrong in citing anything out of that monster thread, the post that I recall mentioned a FTer getting through
landside Fast Track security with an AA elite card and a Y BP (not Flight Connections).
Getting through FCC Fast Track with anything other than a BA F/Biz BP absolutely falls into the extreme exception category - if even that. If I had a dollar for every person I've heard angrily and loudly turned away, I'd be a very rich man... the OP's op-up on LAX-LHR is going to occur more frequently!
Note to BAA: How can you use the same name to describe three distinctly different processes anyway? Each one has completely different rules from the others. Mega-threads pop up all over FT with great regularity trying to explain it, and even then it's incredibly difficult for people to grasp. Clean this mess up!