A lot of times at WH level events he ensemble plays pre and post appearance music like a cocktail hour...then WHCA (White House Communications Agency) has Hail to the Chief...ruffles and flourishes etc pre recorded...there were a couple of events where they prerecorded my intro of the POTUS even though I read everything else live.
IRRC the Marine Corps Band is even less military than TUSAB. They are pros in USMC band uniforms...something tells me this wasn't mistake.
Wow, pre-recorded Hail to the Chief? That's almost as tacky as playing Taps on one of those bullshit digitized bugles.

FWIW, ALL of the D.C. bands (TUSAB, the Navy Band, the Air Force Band, the MC Band, and even the CG Band up in New London, CT) have musicians that are world-class. For any given position that becomes open, there are literally hundreds of applicants who audition. Competition is fierce, even with the height/weight, security clearance requirements, etc.
You don't get in any of these bands unless you're a conservatory/master's degrees graduate and many have DMA (Doctor of Musical Arts) degrees. This means these folks play and sing their asses off.
But I will say that the Marine Corps Band is the ONLY D.C. band whose members do NOT attend boot camp. All other service band auditionees who pass and who are selected for enlistment must attend their respective boot camp/basic training. This is likely why you have the opinion that the MC Band is less "military" than the others.
I saw the Marine Band play once, live in St. Louis about 10-12 years ago. Impeccable playing, but I remember their performance as being very, very mechanical. Little "life" to the performance.
Music is much more than putting the right notes down range at the right time.