In answer to the original questions, no, neither Family Guy nor American Dad represent "real" Statespeople, nor are they meant to. They are both meant to be comedic caricatures of "the American way of life" and American family dynamics. Think of them as an animated sit-com.
(Though some Statespeople I know would KILL to have such dramatic, adventurous lives as the Griffins and the Smiths do.)

I doubt British TV represents the U.S. any better than the U.S. represents any other country. Keep in mind that the goal of most of television is to entertain, not to educate. If you want to get a more factual representation of life in other countries, there are channels like the National Geographic Channel (NatGeo) or the History Channel.

The little I've seen of Statespeople represented in English television comes from Doctor Who, when the Doctor and the gang visited the American Southwest for a couple episodes.
No, not everybody in the Southwest wears Stetson hats (but they are cool!).
No, not everybody eats at 1950s-themed diners every night. (Only for special occasions!)
No, NOT everybody carries around a six-shooter pistol and has insane accuracy (only the Texans).

P.S. Please note that the comments made above are for entertainment purposes only, and are not intended to provide a factual representation of life in the United States of America, either in the Southwest region or any other region of the country.
Because apparently it needs to be said.

I don't watch television.
Is 'Misery' a series?