"Now be honest, was that really improv?"
I haven't heard this song in years, and I don't think I've ever tried to play it. I played this after just a few passes through it to get the progression. I don't even own a copy. I had to download it last night.
This is what knowing some theory and the key can do!
Actually, Sitting on the Dock of the Bay is not the best song to pick for illustrating the theory of chords in a key. Mainly because all the chords are major--every single one, no minors. So the whole thing about which triads you use over which degrees of the scale breaks down.