You guys are confusing "manners" with "etiquette."
The lessons involving using a knife, fork, with a napkin on the lap is etiquette, and it is obviously culturally biased. (Since many cultures don't have forks,) Of course, the argument can be made that the children should learn about American culture.
Manners have to do more with polite behavior. How to treat the servers. Don't double-dip. Don't talk and chew at the same time, etc.