Yeah, Billy, I think you're probably very close to what the song's about.  Something weird about this song... when I was a little kid I always loved it... one of those songs that was sad, but sort of made you happy in reminiscent sort of way I guess.    I couldn't have had a clue as to what it was about at the time.
When I got older, I found out that my older brother used to play that record over and over after his father died (my brother was only 3 years old at the time 

 )   It reminded him of his dad for a few reasons I guess.    I always thought that was weird that I had liked it so much and so had my brother, for  different reasons.  After my brother died, it's meant a lot to me.
When I was in college, there was one  fraternity in particular that we hung out with a lot.  They had a big party at the beginning of the year, and then another one  towards the spring.  (And possibly a few in between 

 ).    The night almost always ended with the last few party-goers (usually members of their fraternity or ours) singing along to this song (the version that goes on forever).  Kind of a strange bonding moment between friends.
So that song still makes me happy in sad kind of way.