Actually, I can recall one instant where it was VERY American hahah.
I was watching Asobi ni Iku Yo!! a while back, and I recall this one very minor scene, where some American Marine (?) was in a car with some chick and got attacked.
The way he said "SH*T!" and "ariGAHtoe mahRHEEkoe" was absolutely American lol. It's probably the only time I can recall an "American" or "native English speaker" in anime sounding exactly right lol.
There are some attempts at imitating a foreigner's incorrect pitch accent (like Michael the fudonshi guy from Ga-Rei and Ga-Rei Zero, or Catherine from Gintam