Their Understanding English with the Accent They Have

This is only anecdotal, so I've got to check it out, but it's my impression that students understand English spoken in the accent they have when they speak English better than they understand English spoken in an accent they don't have.  For example, Chinese speakers understand other Chinese speakers in English better than they understand Spanish speakers in English or Russian speakers in English.  This is true only of heavy accented English, not with nearly-perfect.  (And I'm not really sure it's true of them.)