Yes, the Philips bio is great indeed, have it! Point I was trying to make about neither of those esteemed gentlemen being guitar players is that their observations about guitar players might not always be exact.
King didn't play much rhythm if at all, especially once he could afford larger bands - the couple of times I've seen him he had a rhythm guitar player in the band, so why would he? I especially love his pre "live at the Regal" work, and there are quite a few surprising little moments in there, where he plays some pretty sophisticated Charlie Christian inspired arpeggio lines, comps some very nice chords behind someone else's solo, etc...
While this seems to contradict what Philips said about him, it doesn't necessarily - if you listen to King's recorded output chronologically, he gets better and more sophisticated at a pretty fast pace throughout the 1950's. The recordings Philips made do show he was a little more primitive and crude at that time, but he got a lot better very quickly. His style changed too, early on he was one of the many T-Bone Walker imitators of the period, and his leads were largely minor pentatonic, almost no bends, no vibrato. But that changed into a much more sophisticated and idiosyncratic thing within just a couple of years.
I bet he mostly didn't want to play rhythm behind his vocals - in the Sam Philips days, he was probably too green and scared he might screw up, and not much later, there was absolutely no need for him to play rhythm in the larger bands he had. But with his chord vocabulary, sense of timing and level of sophistication by the late 50's, I'm pretty sure he could - he plays lines and chords between/interwoven with his vocals that are a lot harder to play than basic rhythm.