There does indeed seem to be a section of the exhaust plume from the F-1 engine that is objectively dark. It's visible in at least two Saturn V launch photos I have in my possession, as well as the famous footage you described above.

That would be interesting. Any way you could scan those photos? I've only seen this effect in the underexposed photos. I'm reluctant to comment further until I can see what you're looking at.

But wasn't pogo a problem mainly with the second stage?

Come to think of it, you might be right. I'll have to go scour through the S-5 performance reports and make sure.