The short answer is yes. The founding leaders of the BOS descended from members of the Pre-war united states military. Though things are not that simple.

Lore:
The founding members of the Brotherhood were originally U.S. Army soldiers stationed at the Mariposa Military Base. The founding member of the BOS, Captain Roger Maxson served as the bunkers second in command under Colonel Robert Spindel serving as the Bunker Commander and highest ranking officer on site. Mariposa was home to the testing of F.E.V. (Forced Evolutionary Virus) with P.O.W.'s being used as test subjects. On Oct. 10 when Maxson and the rest of the soldiers found out about what was going on in the bunker, they were horrified. This resulted in Col. Spindel committing suicide 5 days later and morale in the bunker dropping like crazy. This left the bunker in Captain Roger Maxson's control as he was now the highest ranking officer on site. to gather more information on just what was going on in the bunker, the soldiers interrogated Chief Scientist Robert Anderson. After learning about what the they had done, Maxson executed the entirety of the science team. Roger then after declared himself a deserter and we can presume the other soldiers followed. Maxson on the radio announced himself to be a deserter on Oct. 20  and two days later the Great War happened. A couple of days later and the Bunker inhabitants cleared out and made their way to Lost Hills and effectively formed the Brotherhood of Steel as all know today.

Summary:
So yes to summarize the forming members of the Brotherhood of Steel were descendants from the U.S. Military. The only difference is that these soldiers were rouge deserters who had committed acts of treason against the U.S. The "actual" remnants of the U.S. Military were incorporated into the Enclave. So when someone says the the Brotherhood of Steel are the remnants of the U.S. Military, they make it sound as if they are the direct descendants of the U.S. Military, not just low ranking soldiers in the Military who went rouge. They are remnants but no longer share the same ideology of the U.S. Military. To properly say it would be that they are rouge remnants, not the remnants.  

Thought I would do something like this for my 100th post. Hope you enjoyed reading and learned something new about the lore. If I got anything wrong or made any errors please by all means call me out on them so I can fix them. 

But do you guys agree with this? Do you even consider them proper remnants? or just "wannabes".

If you guys want to read up on the lore check just search up Mariposa Military Base on the Fallout wiki.