Interesting timing on the thread revival. I just finished reading Brian Wilson's autobiography and seeing this thread prompts me to think of how some of his solo albums include re-recorded versions of Beach Boys songs (for example, Imagination features "Let Him Run Wild" and "Keep An Eye on Summer"). Does that count as a cover when he's the guy who wrote and composed the songs in the first place? I suppose his live album contains a ton of Beach Boys songs, but I wouldn't count that because it's pretty normal for a former member of a band to play that band's hits while touring.
I guess that raises the interesting question of whether his release of Smile might count as a cover album since the original Beach Boys album was, infamously, never released unless you count the 2011 boxed set The Smile Sessions; also, on Brian Wilson's version, he used the original lyrics for "Good Vibrations" rather than the lyrics made famous on the single released in 1966. I wouldn't think any of that counts as a "cover."