I believe you are on the right track. What I’ve always heard, and later found this definition:
“In music, a “breakdown” is part of a song in which various instruments have solo parts (breaks). This may take the form where all instruments play the verse together, and then several or all instruments individually repeat the verse as solo parts.”
So with “Foggy Mountain Breakdown,” the fiddle gets a break, the dobro gets a break, and the flattop picker gets a break, as well as the banjo.
You must have heard some songs where someone says, “Let’s break it on down, boys!” and the slip into the instrumental portion of the song…and everybody gets a break.
You’ll even find breakdowns in heavy metal, punk & disco/dance music. I was going to post an example here, but nobody really wants to hear it!