Elvis Presley's rendition of "Always On My Mind" was one of several covers of the song released in 1972. It's just that Elvis' version gets the most airplay. The song's actual title is "You Were Always On My Mind", but those first two words were cut out when the single was released by RCA.
The following clip was also used in the documentary, "Elvis On Tour".
10 years later, Willie Nelson, a former label-mate of Presley's at RCA, hit #1 on both the pop & country charts with his version. By that point, Nelson had switched labels to Columbia, which, oh, by the way, was dominating the pop charts at the time along with sister label Epic, thanks to the likes of Billy Joel, Bruce Springsteen, and Michael Jackson, among others.