Brilliant Mistake (live in studio)

Does any Elvis Costello fanatic know how this track should actually be labeled? In the liner notes of this Rhino Compilation it says it's by "The Costello Show featuring his Confederates".

Is that accurate? If so, should the title of the track remain "Brilliant Mistake (feat. His Confederates)" as it does now, or is the full text the actual name of the "artist", i.e., the artist field should be "The Costello Show featuring his Confederates".

Or should the artist simply be "The Costello Show" and the track "Brilliant Mistake" --> without (feat. His Confederates)

This song, and Indoor Fireworks (which is found on disc 2 of this compilation release and titled the same way in the liner notes) is from Costello's King of America album.

Discogs has the reissue of King of America as being by "The Costello Show"
http://www.discogs.com/release/1127738

I have also seen it argued that this was essentially a solo release and the artist should just be "Elvis Costello" which is how MB has The King of America labeled:
http://musicbrainz.org/release/f9a02637-c31a-42da-b35e-4380cd652c3b.html

Wiki says it was billed as "The Costello Show featuring the Attractions and Confederates".
http://en.wikipedia.org/wiki/King_of_America