I'm not a server guru, but my understanding has always been that relative links are more efficient. (Stands to reason, since absolute links require the browser to call up the domain with every page change.)
Relative links also save bytes (albeit not many), simplify offline testing, and help to avoid broken URLs if pages or directories are moved.
I haven't seen any evidence that Google has trouble following relative links. The fact that GoogleGuy isn't suggesting that people change their relative links to absolute links indicates (to me, anyway) that there's no compelling reason to do so.
IMHO, there's a natural human tendency to look for quick solutions when things go wrong, and I know Webmasters who have rushed out and made changes that haven't proven helpful (and, in some cases, have been detrimental) just for the sake of doing something. I suspect that "change your existing relative links to absolute links" is a good example of a placebo disguised as a panacea.