I'm not going to argue with you if you want to call neural nets AI
Personally I do not think they qualify as intelligence. Neural networks are a (partial) solution to enable computers to learn, in particular to learn from data and optimize their behavior to accomplish some goal that wouldn't have been possible that effectively using programming. Neural networks are not that different in principle from stuff like Markov models and so on.
But I would say intelligence is more than the ability to learn. Most importantly, it is the ability to solve new problems, including abstracting known solutions to apply them to something else. That is really outside the scope of neural networks.
I think neural network is a specifically problematic term because (and that is not directed at you) many people assume that because they are inspired by the human brain, they have the potential for the same abilities as the human brain.