Anime is short for Animeeshun... The Japanese word for all Animation.. Joe from Family guy to the Japanese is indeed anime.
SO it counts.
What?! Really? O-o"
Yes really if your talking to a Japanese person or someone that at least understands Japanese and Japan enough know all animated cartoons are known as anime in Japan.
Now if your talking with fad followers who think Japanese Animated cartoons is something Magical to be above all other cartoons.. then they will fight tooth and Nail against that.. even if they have not a clue of the facts.