I disagree there, I think the MWBOS were more removed from the Original BOS than Bethesda's. The MWBOS turned into a power-grabbing organisation looking to dominate the people in its area. They accepted Ghouls, Mutants, and even creatures that had no relationship with humanity into their ranks.
However, the MWBOS had a different answer to the same question - How to ensure long term structural survival - Manpower and food. They created a fudal culture with themselves at the top. The EBOS created a semi-removed from society warrior cult, that didnt go for the same extreme measures as the MWBOS.
Indeed they were removed, but this was an intentional decision by the Lost Hills faction. The MWBoS wanted to accept tribals into the ranks, whereas Lost Hills wanted to remain 'pure' so put some distance between them, ordering them to wipe out the remnants of the Master's army. The only reason Lost Hills was so xenophobic toward Mutants and Ghouls alike is because the Master's army set the impression on which all other mutants would be judged, and the ghouls that scavenged the West Tek are the reason the BoS have disdain for them too. But beyond that, there's no reason why any prejudice would endure. So it's no surprise the expansionist MWBoS sought assistance from them also.
If the fleet wasn't so unfortunate as to get downed and scattered by the electrical storm, there would have been little reason for them to employ a means for survival in the first place, it was this blunder that forced them to work with the local populous and from there they became self-sufficient.
Indeed. When we look at the differences between the Eastern and Western chapters of the Brotherhood, the overall goals aren't that dissimilar, it's just the ways they go about it are different.
The Eastern Brotherhood wanted to secure the Citadel (And what was located within the Citadel) as well as continue to locate technology. The Super Mutants were and are searching for something in the D.C. Ruins, which is alarmingly close to the Citadel itself. Given the nature of the prize of the Citadel, I can't fault Lyons decision to push back the Super Mutants.
However, it's obvious Lyons decided to take this one step further, by assisting all the outlying Wasteland, in the attempt to make the region stable enough that the Brotherhood could continue its primary mission relatively peacefully, with minimal loss of life.
It's tough to decide what the Western Brotherhood would do in similar situations, because there was nothing quite like what the Eastern chapter found beneath the Pentagon, and they didn't face the constant threat of Super Mutant incursion since it's virtually impossible to stage a successful assault on the Lost Hills Bunker since the Elevator can only hold so many at once. Also the Lost Hills Bunker is a lot more removed from "Civilization" then the Citadel is, so it's easier to be Xenophobic and "Elitist" when you don't witness the suffering of the Wasteland every day.
Really, the Lost Hills Bunker provided the Brotherhood of Steel the same kind of isolation that a Vault would have.
EBoS secured the Citadel because of what they found there, and the structure had the makings of a fortress, evidently. They would have continued to locate technology had Lyons not allocated his manpower into the preservation of civilian ideals such as Project Purity, and then sparked a feud within his own ranks and lost vital manpower and tech because of the ill assessment of his goals. It wasn't then, a case of assisting the local populous in the scheme of BoS's primary mission in the region. There is no hint of this in D.C as all the BoS are simply policing the mall and GNR. A scribe with a couple of bobyguards in a library hardly proves any prolonging resolve in the preservation of knowledge and technology.
Lyons lost more able men and women by reassessing his goals through bloodshed and mutiny than if he had adhered to a strict and methodical scouring of key locations to get what they needed so they could retreat safely within the confines of the Citadel and do what they set out to do in the first place. At least if this primary achievement was satisfied, maybe the appeal of outside help wouldn't have been such a farsight, but it would still be a purely quid pro quo scenario, and definitely not what Lyons had intended.
It was also seemingly impossible to stage an assault on the Citadel, it was just as secure as any bunker, and the BoS within seemed more than safe, especially when you compare them to the minced squads based in and around the D.C ruins themselves. Lost Hills was as removed as they wanted to be, and this could have been an option for Lyons if he chose it.