Davis absolutely hates wheat, on very justifiable grounds. And he strongly recommends anyone with heart problems get off it immediately. But I dont think he has anything against rice.
Actually, if you read his blog, you'll find lots of articles that, at least indirectly, indict rice (and basically anything that spikes your blood sugar, which includes all grains). For example:
Generally, he advocates close postprandial monitoring of blood sugar as a sort of proxy for triglicerides/ldl and often notes that some people may have higher tolerances for certain foods than others. If rice doesn't raise your postprandial blood sugar much, then I'd imagine he'd be ok with it.