My take on the new BOS incarnation:
The DC BOS is a case example of how distance from civilization will cause variations in interpretations of accepted and dictated behavior. Taking the settings of both Fallout: Tactics and Fallout 3, the theme of the eastern part of post-apocalyptic USA is that it is the new wild west much akin to the 1800's wild west. Law and order is self interpreted, and civilized implementation is rare but distinct, and typically under assault from those that would like to take advantage of the environment.
In the 1800's the US Army had posts spread out in the western territories, and as was the case in the east, they were not established there to enforce law and order, but to protect American property and interests. If the Army outposts became involved in local law and order is if a soldier had been involved or if conflict was brought to their front door, otherwise according to Army doctorine they would refuse involvement and take no action in the situations.
However, due to the distance from the civilized east (both in miles and in communication), and the govenor-esque caveat of "your word is law" akin to naval vessel captains of the time, Army post commander had the legal flexibility to be as much or as little involved with the local community in the interest of keeping their post functional and operational. As a whole most post commanders were indifferent and simply maintained a trading post, while some abused their position for self gain securing comforts for themselves and their men. However some commanders took it upon themselves to act as law enforcement and protectors of the land, beyond fending off Native American attacks. Examples are the endorsements of bounties on criminals (which normally would fall under the juristiction of townships) and detactments of soldiers to townships to maintain law and order. The only thing keeping a post commander from violating the UCMJ and Federal law outright was that with established (but limited) communication to the civilized East, word would eventually reach Washington and appropriate action by the US Army would be forthright.
To return to the Fallout universe, FO3 is the first case of the eastern expansion of the BOS to have actual periodic contact with the West Coast BOS, where as with Fallout: Tactics the BOS faction there lost complete contact with the West Coast BOS. How they got there is specifically up for debate, but entirely unfeasable (Airships aside). Using simple travel means like Oregon bound settlers of the 1800's, coast to coast travel could take up to about a year or slightly less using ground travel, which is more likely than Airship travel. As for contact with the West Coast, considering this expedition was a genuine BOS back endevour, I could see part of mission east involved setting up manned or automated communication relays, so as to avoid the communication blackout the BOS faction from Fallout: Tactics suffered. With communication set, constant reminders as to the mission and purpose of the BOS's directive could be reinforced.
For the major point of contention, the shift in priorities of the DC BOS. As mentioned above, distance plays a major role in the inherent moral and duty flexability of an isolated detactment of an organization. While they were audiably present in progress checks and reports, the Elders of the BOS were not present or able to watch everything the detactment was doing. Timeline and results were the checkpoints the West Coast BOS's needs. Beyond that, so long as those objectives were being met, Lyons could do whatever the hell he wanted within reason and "good judgement" that reflected upon the values of the BOS.
We already know that Lyons was an idealist and more progressive than his peers, so with distance as a factor and the ability to call his own shots without the Elders interference, Lyons set himself and the DC BOS up to shift from classic BOS Illuminati mentality to a more Arthurian mentality. This was not an overnight decision as explained by BethSoft, but rather a gradual exposure to a vacant niche in the environment of the Capitol Wasteland, specifically a semblance of established law and order, as opposed to self-interpreted law and order as the Capitol Wasteland was previously accustomed to. The stereotypical "Knights in Shinning Armor" tag is a result of the priority shift, not a catalyst. It remains to be explained, however, just how much of an impact the DC BOS priority shift had on the locals, seeing as Megaton is a longstanding community exsisting before the expedition, and the general social setup of the pocket communities law and order to be self-enforced.
Devience does result in awareness however, as more than likely conservative soldiers in the DC BOS began to report Lyons' deviant behavoir to the West Coast BOS behind Lyons' back, as while Lyons is honest soldier he would not do anything to bite the hand that feeds him and cause whatever aid the West Coast BOS provided to be witheld. With the wistle blown, it is likely the Elders called Lyons on his bluff, and Lyons confirmed their reports (fears) that he was using the BOS resources to further his agenda for stabilizing the reigon's community than sticking with his primary objectives. This is what led to the "You're still BOS but you're on your own till you get back on track" decision from the Elders, though the "till you get back on track" is more of a hopeful opening for Lyons to stop playing Vault Dweller and come to his senses than a tangible objective.
So, is this a feasable deviation from previously established BOS doctorine? I would say yes it is. It follows the prior example Fallout: Tactics used to explain its particular devience of distance allowing changes in priorities and method of operations. While the BOS is an organization with strict ideals, it requires close proximity to enforce these values, otherwise they are just guidelines and suggestions, rather than commandments with the wrath of God backing them up. Beyond Fallout 1 and 2, there were templates and designs to alter a faction of the BOS to a far more xenophobic organization than the prior incarnations, but that is simply stereotyping one aspect of the BOS we know. The DC BOS is simply a stereotyping of another aspect of the BOS, being a solid and involved foundation of the future of the Wasteland.
Hope that all makes sense.