In this case, the speaker cannot, through no fault of his/her own, make it clear what he/she wants because of his/her accent. Ergo, he/she cannot **distinguish **between the two, to the satisfaction of the listener.
Perfectly legitimate use of the word distinguish, if you ask me.*
*And I am, if you check my profile, a cunning linguist.
Here’s an interview with Andy Cowan, a former contributor to the show (he’s the guy who came up with “The Opposite,” in which George ignores his instincts and does the opposite thing). Some of Cowan’s never-used ideas appear as bulleted points below the “The Puffy Shirt” etc. headline near the end of the story - some of those could’ve been pretty funny, I think!