This is a theory I have to explain the apparent BoS presence in Fallout 4. It's like 90% speculation, so take it at face value.
First off, I'm making three assumptions; The the BoS in Fallout 4 is from the CW, as implied by the name of the crashing ship being the name of King Arthur's ship, that the Lone Wanderer told Lyon about the Super Mutant's home in vault 87, and that the 200 years bit was a generalization.
So we know Arthur is meant to take leadership of the BoS. But how and to what point? The CW chapter has all but been excommunicated due to Lyon's actions, and even then the BoS is not doing well on the west coast due to the conflicts with the NCR. Basically, Arthur is a destined king of a dying empire (as it were). I believe that his rise to power isn't a good one. He get's older and starts to question Lyon's actions and abandonment of his ancestors codex. Eventually he makes his move to become leader but finds little support and Lyon's doesn't want to step down as he feels Arthur will undo all Lyons had done (help the CW). With so many local recruits, Arthur doesn't find many who will support his claim.
He leaves for the Outcasts, basically true BoS in all but name (maybe some of Lyon's flock goes with him as they still support the old brotherhood). Arthur promises to restore the eastern brotherhood and reunite them with the west coast. The outcasts lead an assault on the citadel and Arthur becomes the leader of a united CWBoS, with Lyon and his loyalists exiled. NV mentions that there was a civil war in an eastern chapter, the the outcast leaving wasn't really a civil war in that there wasn't really any fighting when they left. NV is set a few years later so this may have been when Arthur attacked in a proper civil war?
With the salvaged Enclave tech (like the Rockland Relay), he contacts the MWBoS and they form something of an alliance and share knowledge (MW gets reverse engineered Enclave tech and CW gets airships). Arthur knows he needs to expand his territory, so he sends scouts to find a good target.
At some point he learns of MIT and their synth revolution problems (fallout 3 hints that more and more synth's are seeking freedom). He knows of their advanced tech and sees this as an opportunity to strike while they're distracted. With the MW airships and the Enclave tech, they launch an invasion.
I think in the game, Beth will do what Obsidian did with NV and say that the army is small because they're involved with engagements all over, not just in Boston. Maybe the MWBoS learns of the CW plans and doesn't like the idea of them getting tech that powerful, so they attack them over it?
Any thoughts?