If you want a "fresh and neutral" faction you don't use the Brotherhood of Steel at all. Using the Brotherhood of Steel is always a way of drawing upon their appeal from previous games and in Bethesda's case this will be Fallout 3 and Lyons. Going back to Tactics for the Brotherhood of Steel when you already have a group your playerbase knows and that you went to some trouble to bring over to the East Coast in the first place makes absolutely no sense.
You don't need to spend a separate game setting that up as New Vegas showed with the completely unheard of Legion and House and for most of the Fallout 3 fanbase the NCR. For Bethesda to bring back the Brotherhood of Steel and not have it be Lyons would be like Obsidian having the Brotherhood of Steel in New Vegas only for it to be a group of Lyons' guys. It doesn't make any sense.
From everything we knew about the Brotherhood of Steel their sudden appearance in D.C. made no sense either until Bethesda threw a few sentences together justifying it. I don't understand why this move would be such an incredible unbelievable step even if we accept that it is literally however long after the war and not just an approximation of the actual date. Maybe the Brotherhood is going up to Boston to see if the Institute can provide them with the assets to fix Liberty Prime or track down the person who helped them get it working the first time and they found the airship designs in Eden's dream diary. Or they just built them as Tactics so elaborately explained. There you go it already makes more sense than the initial move to D.C.
Again there is no way of avoiding that the argument for the Brotherhood being from Tactics rests entirely on the airships and we already have a clear example of Bethesda reusing a Tactics asset without it having any in universe connection to Tactics. Not to mention that its at least as baffling for the MWBOS to have vertibirds as for Lyons to have airships.