I wonder who produced/contracted those RCA sides. The sidemen are more than a little "high class" on a consistent basis. This isn't the usual case of the odd jazz player or two showing up on an R&B date. This is definitely an arranger/contractor/producer/somebody calling in top-shelf players to cover what for all intents and purposes are "normal" R&B charts. There's definitely a difference in feel and execution as a result. Subtle, but real. Not necessarily "better", but definitely...different, and not at all in a bad way.
I have the Greer Bear Family set (tho I haven't listened to it in a while). The booklet with that lists the producers on his RCA sessions as Stephen H. Sholes (with Charles R. Grean for two sessions) from 1949 thru April 10, 1952; then Joe Thomas - a tenor saxophonist and vocal coach, but not the Joe Thomas who played in Jimmy Lunceford's band, later recorded in an r&b style for King Records, and, years later, made a recording for Uptown Records - Danny Kessler, Ed Kissack, and Bob Rolontz.
It's possible that the presence of some of the sidemen was due to the influence of Lucky Millinder, who is listed as the band leader on several early John Greer RCA sessions. Greer played in Millinder's band. Greer himself, pianist Howard Biggs, who was musical director for The Ravens, and Leroy Kirkland are listed as leaders on later Greer RCA dates.
As Jim noted, many well known jazz musicians - among them Rudy Powell, Mundell Lowe, Al Casey, Tony Scott, Tate Houston, Art Blakey, Seldon Powell, Aaron Bell, "Skeeter Best, Earl May, Idrees Sulieman, Eddie Barefield, Buddy Tate, Taft Jordan, Jimmie Crawford, Budd Johnson, Jerome Richardson, Billy Taylor (pianist), Connie Kay, and Tyree Glenn - played on John Greer's recording dates, though that wasn't all that unusual in the early days of r&b.
Hope this helps a bit.