Vous avez tout à fait raison Diane! You are correct Diane, the grammar is in fact incorrect and I understand exactly where you are coming from.
Our justification for having translated it this way is that it makes things simpler but also by using the expression "Tu peux me tutoyer " there should already be a sense of familiarity with whomever you are speaking, and in these cases we would rarely use the word 'may' in English. To illustrate my point here are two examples:
"May I speak informally with you?" --- "Yes, you may."
"Can I speak informally with you?" --- "Yes, of course you can!"
The word 'may' carries a fair degree of politness and in order to ask the question of being able to speak informally, you should already have passed that level of politness. Our translation was meant to capture that familiarity and overall sense of the phrase and I'm very sorry if it has caused confusion. I hope the knowledge that grammatically you are correct is some consolation.
I hope this helps,