Speaking as an ordained minister who has conducted far more funerals than he'd have liked to, I have some experience in this area. I've had many volunteer veterans groups do a wonderful and dignified job at gravesides, and I've had some beery bozos and so-called "chaplains" make a hash of things.
In the end, it's the family's call. Unfortunately, it is the nature of things that many families are too bound up in their grief to know what they're getting, and all too many folks -- funeral directors as well as volunteer groups -- are eager to act on what they presume the family will like. We clergy are often unconsulted about the arrangements. Funeral directors think they "hire" us to show up and do whatever we do at the appointed time in the funeral they're selling the family. Veterans groups sometimes come in and basically do the funeral over, reading from a superfluous script things that have already been said. All said and done, though, most funerals go okay, no matter who's doing what; unless things are really badly handled, people remember things that touched them and forget what didn't quite make the grade.
But if the veterans groups that think that it's about THEM think I'm gonna take up their cause in the name of religious freedom or something, they've got another think coming. 'Cause nobody's keepin' ME from saying the great Words, and I'm the guy what's charged with sayin' 'em. If my freedom isn't being abridged, then who are they to say theirs is?