Do you think that an accent indicates poor communication skills or the inability to understand each other?
No. But a heavy accent has a effect on communication. I don't like to have to ask a doctor to repeat himself because I of an accent.
And For those who American English is not a first language there re always some issues with idioms and vernacular and subtleties are missed by those for whom English is a second language.
When i go to a Doctor I am there for one thing; my health. I am proactive in that area and if there is any impediment to communication and understanding then I avoid it.
Hell If I were practicing medicine in France and I had only been speaking French for a few years I would understand if someone would choose a native Frenchmen for a Dr.