I think the article touches on a few interesting points, but only at a fairly shallow.
What I have noticed working with various levels of bilinguals is that native vs non-native often have different misunderstandings.
A native person firing something off to another native will make too many assumptions. "I understand what 'it' is. No need to elaborate" is the feeling.
Non-natives tend to lean on a smaller set of vocabulary and grammar. This tends to serve them well in slower, written communication but can give them trouble in speaking when there is a miscommunication and they don't have the skills to correct it. Over- or under-applying a rule past it's breaking point. They also have to contend with false friends(words to be related across languages but actually have different meanings), which can sometimes cause very hard to spot miscommunications as both speaker and listener have separate but consistent ideas in their heads.
When it comes to accents, in general it can be considered rude to ask someone to modify their accent. I know that if I affect a general American accent I will be understood better, but should I?