"If a teacher speaks incorrectly, they are more likely to write/spell incorrectly "
awaywiththefairies, how did you make that particular giant leap?
I drop my aitches sometimes. I might say "I 'aven't done that yet" although I try not to.
Are you seriously suggesting that I am more likely to believe that "haven't" is spelled "aven't" than someone who was born in Kensington?
What an utterly ridiculous thing to assume.
It is quite right to correct a teacher's written errors, if they are as bad as "would of."
However this thread is about spoken pronunciation - what the teacher said, not what the teacher wrote.
Unless you can find evidence that the teacher wrote "anyfink" or "anythink" then there is absolutely no way you can claim that "this is not an accent issue." It cannot be anything other than an accent issue as it was about how the teacher pronounced a word and nothing has been said by the OP about how she spells it.
By asserting that people who cannot pronounce things to your satisfaction will therefore be less likely to be able to spell things to your satisfaction, you are committing an act of pretty stunning prejudice.
I think you need to take a long hard look at yourself and what you truly think.