Agreed on most fronts, but I don't think any contradiction occurred by the RB spokesperson against anything Horner has said.
Horner's original quote reported by Daily Mail:
"We have had several conversations over the years about Lewis joining. They have reached out a few times. Most recently, earlier in the year, there was an inquiry about whether there would be any interest."
He never says it was Lewis or his management. He says "they have reached out a few times", meaning someone that is a representative for Lewis.
If Horner was approached by Anthony Hamilton about Lewis joining the team, personally I think it's logical of Horner to assume that this approach is on behalf of or at least has been sanctioned by Lewis (given that Anthony is close to Lewis and used to be his manager)
Horner on the same topic to a different outlet, RACERmag:
"It's only natural that the people around him would reach out at some point in time."
"He's had a tough year; prior to him re-signing with Mercedes it’s only natural that the people around him would reach out to see what the options are. There's nothing unusual about that, it's something that's happened in the past and it’s not unique to Lewis."
The story doesn't change, it's just that it's possible Horner believed Anthony Hamilton spoke for Lewis when maybe he didn't