I think it is short-sighted to call Chet Atkins a country musician (although he often called himself that). In the early days, he was a boy wonder on radio. Later when he tried to do the Grand Ole Opry, he was more or less shunned as being too fancy/shmancy with his playing - "all that weird jazzy stuff".
Once he made his mark with RCA, though, and got some power -- he helped a lot of those in Nashville that previously dissed him. Suddenly he was very welcome at the Grand Ole Opry (although country purists still did not like it much).
His main competition for attention in those days was guitar innovator Les Paul. Where Les was all about speed and flash -- Chet was all about tone, harmony and melodic structure. What Chet was putting out then -- even for country tunes -- was very clearly progressive jazz, by definition. Each new verse was a progressive variation of the previous.
Meanwhile, in Nashville he was producing the likes of the Everly Brothers (played on many of their cuts) and tons of others -- both country and pop.
The best description of Chet, though, was the one he came up with -- CGP -- Certified Guitar Player.