So everything I've read, including from Google themselves, suggests that having two <h1> tags on a page, so long as they're relevant and not abused, does not impact negatively on SEO at all.
So for example, one <h1> for the website title/logo, the other for the page title.
However I am currently working with an Aus based SEO professionally that is very well regarded in the industry, and he is strongly insisting that it does make a difference, and that he very strongly recommends only having a single <h1> tag.
I'm loath to change my view without some evidence to back another view up, of which he has none, so what do folk think?
Where have you found info that says that accessibility would be different from what google recommend? Most sources I have read outline that if you're using HTML 5, and so grouping your page's content elements in <article> tags, for example, that the most correct first tag within an <article> tag would be <h1> (or <header> if you want to be even more "correct")