It's a reference to the music of Bill Monroe, Paul. I think he coined the term to describe what his perceived notion that "Bluegrass" music should sound like. And since the genre' is largely recognized as his creation, (I would argue it was the perfect confluence of several factors...) it was his prerogative I reckon.
Jerry Garcia was very much influenced by that sound, as were many others. Sure enough, there's a lot of first generation bluegrass found in Grateful Dead music. Not too coincidentally, there's a fair amount of Grateful Dead music crossed back over into the modern bluegrass scene now.
How we got to here was, I derailed Dave's thread by griping about Vince Gill winning an award for a bluegrass album called High Lonesome Sound, that had a total of ONE bluegrass track on it. Leland Sklar played bass on the rest of the album and once I got over myself some years later, I really drew from his playing on it.