Councils refuse virtually all informal challenges, (>95%), because they know most people then cough-up to get the discount option. It's called 'gaming the system'.
There seems sufficient doubt about their response to form a good appeal case, but obviously, you have to forego the discount option. If it were me, I'd be taking them all the way. Councils are notoriously bad at signing parking suspensions, but with people coughing-up so readily, they never get called out.