It's not an adversarial court because its powers are circumscribed to issuing warrants and subpoena orders, which are not adversarial processes in any court (at least, any court in the U.S. that I'm aware of).
You're basically right, but other courts have processes for review of incorrectly issued warrants and subpoenas. With the FISA court, if you were incorrectly watched, you'll probably never even know.
