With a steep rise in the number of foreign graduate students in the last two decades, undergraduates at large research universities often find themselves in classes and laboratories run by graduate teaching assistants whose mastery of English is less than complete.
Of course, the article offers nothing but anecdotal evidence to support that 'often'.
Naturally, I would like to chalk up these complaints to racism. But almost every account given in the article includes praise for the teacher in question: they're called brilliant in their field, but completely ineffective teachers. Furthermore, almost half the grad students in my old department were from China or Taiwan, so I know firsthand that occasionally accents will be quite thick.
The best approach, if departments really feel this is an issue, would be to gather hard data: Are complaints about impenetrable accents clustered around a few TAs? What percentage of a TA's students report problems understanding their instructor? Then maybe a semester in a class designed to improve English diction would be advisable.