Sol would never have gotten an audience with Vito unless another Don vouched for him. "My compliments" was not Sol admitting that he was trying to hide Tatt's vouching for him, it was his way of was buttering up Tom to reinforce Tom's enthusiasm for the drugs deal.
I think you might be letting knowledge of the book bleed into what actually happens in the movie. The book makes it clear that the Tattaglias are sponsoring Sol, but that's purged from the movie. Sol's compliments are presented immediately after Tom reveals the connection to the Tattaglias, so if Sol is buttering Tom then that discovery is what he's buttering him with.
That said, if Copolla inserted this cagey little exchange as a dramatic flourish, he shot himself in the foot. If the Tattaglias DIDN'T ask for the meeting, then Vito never REFUSED them an accommodation, and the war never happened. It was all a dream....
