John Stewart's "Hiding In The Shadows", a Lindsey co-write or not?

[face of glass]

While this reindeer-rider (and no Carne, I won't bring that up again if you won't either ) was over at the http://www.copyright.gov he found this while browsing Lindsey's section:

52. Registration Number: PA-214-719
Title: Hiding in the shadows / L. Buckingham, J. Stewart.
Note: Performed by Nick Reynolds & John Stewart.
In: Revenge of the Budgie. mTakoma TAK-7106, c1983. 1 sound disc : 33 1/3 rpm ; 12 in. side 2, band 2
Claimant: Now Sounds Music
Created: 1983
Published: 1Dec83
Registered: 14May84
Author on © Application: music: Lindsey Buckingham; words: John Stewart.
Special Codes: 3/M

I was never aware of this since even Nancy's BuckinghamNicks.net only lists LB as a guitar player on that tune, not as a co-writer. Even the All-Music Guide didn't know a thing. So this is for those who have an officially released version of the song; is Lindsey given a songwriting credit in the album notes or not? And is this another spin on "The Chain" riff? [Because I haven't heard the song.]