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Yes.
There are separate and distinct approaches but they are connected and IMO "old time" for what ever that definition is worth :)
I would think of the distinctions as..
Piano rags "Classic"...

"On one hand, Southern Flavor is one of my favorite tunes to play. I play the lead very differently from Monroe's way of playing it, but the melody and chord progression of the B part are always...

While not transcribed, there are some slowed down versions of Son Huasteco fiddle tunes to be found here:
http://www.oldtownschool.org/connect/fiddleclub/page/14/

I respectfully disagree that the "Circle" project is sub par. Perhaps another close listen would change your perspective. As to the musicians not being up to Monroe's standards...well...Ol' Bill hit...