The researchers suggest that it isn't just down to prejudice, but might have something to do with what they refer to as the "fluency effect" (Wikipedia defines and explains it here). Perhaps if we struggle to process a heavier, less familiar accent, we tend to believe the content of it less. The study referred to by the BPS seems to suggest that the fluency effect really has an impact.
A while ago (1971 to be precise) Howard Giles carried out a famous sociolinguistic study when he looked at attitudes towards different accents in the UK. He used a matched guise structure for his study (read more about this methodology here) and the American study is similar in many respects.
Edited on 26.11.10 to add:This piece of research into the brain's activity when faced with foreign accents is also quite interesting.