I have to say Bruce Wayne is mistaken if he thinks he's proven Doc Savage leads with his left; Doc was holding a drink in his right hand, he could strike just as well either left or right.
It's funny to see Doc with white hair (and eyebrows), but I put that up to the Bama look on the paperback reprints. If nothing else, it makes him stand out compared to everyone else.
And I'd bet Doc has figured out the Batman double identity already. He mentions that he didn't smell alcohol on Wayne's breath, which is a hint that something fishy was up. I'm biased a bit, but Doc was certainly at least as observant and analytical as Batman at any point.