Earlier quoted context omitted.
In their defence, in Section 15 of the FOI rejection letter, they mention the software is used for several fee-for-service industrial elections.
They still have copyright on the software: copying it and, say undercutting the AEC on the fee-for-service would be illegal. Far more likely that the AEC don't want to have their software open to scrutiny by politically-motivated geeks.
So they have a protected monopoly for that too?