Ahhhh, the part about EXPORTING it out of the US is very wrong. Americans aren't "free to do as they please" when exporting. The American can take with him a small amount for personal use outside the US, for hunting or competition. Not to sell or give away. As such, it would also have to be the American that declares the ammo bringing it into Canada. (export/import occurs simultaneously, if he gives it to you at the border for you to import, then he is exporting and requires a permit.)
EVERYTHING else requires a US Export Permit, which can only be obtained through a US exporter registered with the US State Department.
I recall recently reading a couple stories on here where Canadians trying to import ammo without permits have been turned back (or you could just surrender the ammo)
A far as a Canadian purchasing and possessing ammo in the US, no problem as long as you have a hunting license from any state, or an invitation to a qualifying competition.