Is it true that any speed limit over 80 mph is a felony in Arizona?

It depends on some specific facts and the specifi traffic violation for which you were cited. However, an Arizona statute on excessive speed, A.R.S. § 28-701.02 states

A) A person shall not: 

1. Exceed thirty-five miles per hour approaching a school crossing.
2. Exceed the posted speed limit in a business or residential district by more than twenty miles per hour, or if no speed limit is posted, exceed forty-five miles per hour.
3. Exceed eighty-five miles per hour in other locations.

 B) A person who violates subsection A of this section is guilty of a class 3 misdemeanor

The laws are different depending upon the area where the person is driving, the type of vehicle she or he is in as well as whether that person was racing.