Deane,
After watching a number of clips on Youtube, I will have to say you are far from wrong. It looks like it was a fashionable thing years ago for many well known artists and groups to play the excerpt from Under The Double Eagle. Because of the instrumentation and the style, it does sound like a totally different tune.

It was funny to read the comments for Chet Akins version; one person thought the Chet Akins version was a country tune and said, "This is what country music is meant to be not that current crap!" Another corrected him, "Country music was meant to be a 19th century Austrian march? :))
Yet another said, "You guys are all wrong. It's Sousa. Brush up on your marches folks." Actually, all these years I thought it was a Sousa, too.

Anyway, arranger players can appreciate a well known tune played in a totally different style and instrumentation. I enjoyed all different versions. Myron Floren even had a Disco Polka rendition. What's that??? Well, one of the three links below.

https://www.youtube.com/watch?v=QbcJi5nF03o

https://www.youtube.com/watch?v=SQlgqtfieSs

https://www.youtube.com/watch?v=JF8ib39YObo

"That's a Sousa March. L