This might sound a little weird - it sure got me off guard - but this was very common in that period (mid 50's). In fact, there weren't many singers who did write their own material, but of course there were some exceptions, like Chuck Berry for example.
Elvis was, according to Prof. Covach, a "Song Stylist": a performer who could take a bunch of songs and test them until he found one which sounded completely like his style. I believe he made some adjustments on those too, and made them sound, well, "Elvish"! And that was a huge differential, making him stand out among other singers and becoming the King of Rock we all love so much.
One of my missions in life is to learn some of his dance moves. I don't get how come people don't dance like that all the time. Honestly, guys, Beyoncé couldn't do it better!