Since these "teachers" tell students they can't use 'can' to ask permission, your daughter might simply be extending this to the example in question.
While it is laudable to encourage children to be more polite, why tell children lies about language? These grade three students already intuitively know how the rules work with regard to 'may' and 'can'. They know that 'may' is more polite and they deploy it as needed.
I once told a friend, who is a teacher in a northern state, that the kids just don't follow the advice given them by their teachers on this may/can thing and she replied, "Yeah, they just don't get it, do they?"
I said, "[name], it's the teachers who just don't get it. Your daughter asks you for permission all the time using 'can' and you reply in a completely natural fashion, with not a thought given to the "rule", yet you try to teach this nonsense in school."
Her jaw dropped to the floor, not because of what I said but because of the sheer ludicrousness of this "rule".
Can and may are most frequently interchangeable in senses denoting possibility; because the possibility of one's doing something may depend on another's acquiescence, they have also become interchangeable in the sense denoting permission. The use of can to ask or grant permission has been common since the 19th century and is well established, although some commentators feel may is more appropriate in formal contexts.