Yes, "stolen" is too harsh a term. If you get booed for singing your own song while on stage with willie, Waylon, and Johnny cash, it only means you're singing to a bunch of low-life hicks that would do better pumping their paychecks into a jukebox, that's all. If I was kris I would've taken a dump on the stage and told them 'there's something to clap about!', shortly followed by 'I'm rich byitch!'
Yes, Cocker's got some great covers. However I don't think an artist ever does it with attitude of 'I can do it better', rather an acknowledgment of how great the song is and that it connects with them too. Let's face it, some people are great songwriters and some are great performers. A great recording relies on both (if only Neil young would take heed). Take a look at Townes van zandt, Danny o'keefe, and Leonard Cohen all covered by great performers who would only produce a solemn 'thank you'.