No, it's really not.

Source: while working as a transport planning consultant, I had a private client in Austin. He flew our team around the city in a helicopter, saying "see all this traffic? It's insane!". I'd just flown in from New Delhi. By the standards I was accustomed to, I didn't see any traffic at all.

Certainly Austin does have a need for much better public transit -- and if being upset about traffic is a catalyst for making that investment, then that's great! -- but in that respect it's no different to most other major metropolitan centers in the US.