I think you are right, it is either a triple row or piano accordion.
It just doesn't have the single row sound for one thing. Also, it is played in the key of D, which would have required an A single row, but those would have been extremely rare in the mid 1980's when that was recorded. I have not tried to play it myself, but I think you are also right that there are notes used in the song that wouldn't exist on a single row.
If it was a triple row, it would have had to have been a G-C-F, played on the pull key of the outer row, which is D. But the playing style is so smooth that I think it is more likely to have been a piano accordion. I will have to try it on the triple row myself to see how it might go.
I know this song from one of Boozoo's mid 1980 recordings. That was definately on a triple row. I kinda like Boozoo's version better. I used to play it a long time ago - it might be fun to pull it out again.
This could? be the same song that Leroy Thomas sings on his latest, and IMHO best, CD " Right Now is PrimeTime " and the song is called " I Know Somebody's Cryin' "...trying to get it right on my single row Bb box..it's a bit tricky but the notes are all there....GREAT song..slow Blues tempo.
I don't play triple row so can't comment if it'd be better on one of those beasts!
Lyrics are:
I know somebody's cryin',
Then they cryin' just for me,
I know somebody's cryin',
And they cryin'just for me
Ooh no matter what happens darlin'
I will always, always love you.
I know somebody's talkin,
And they talkin' bout me,
O know somebody's talkin'
And they talkin' about me,
Oooh no matter what the people say baby,
I'll keep on, keep on lovin' you.