There is something I wanted to tell a long ago but kept forgetting again and again, so that's what I noticed one day and found it funny.
Many foreign speakers who study English (myself included) are very curious for different accents, and the more gibberish, the better. Heavy accents from different regions of the country are often considered among foreigners to be the essence of the language. As a result, an ability to speak putting on some native accent and not your obvious foreign one is considered to be quite an achievement in learning (which it probably is).
This habit is obviously based on the fact that people don't speak like that on courses and the only way you can get enough of that experience is to live here. That knowledge makes you different from somebody just learning English in their home country.
What's the funny thing I mentioned in the beginning? The thing is, the best way to dispel that delusion is to listen to some undoubtedly well-educated person, especially if language is their profession. Suddenly you realise that oh my god I can understand everything as if he or she spoke my native language! Oh I didn't think that's possible! No, no, no it can't be THAT easy, WHAT DID I STUDY FOR?
So accents are still very interesting and being able to recognise and understand them indeed differ people with and without language experience. Still, the best and the real English is apparently... yes, the one that your teacher tried to speak. Might be trivial, but took some time for me to accept this fact.
I remembered about that while listening to David Crystal's videos today. See, I'm sure every English learner regardless of their skill level can understand very easily what he's talking about: