If this was a case of turning up for arbitration, sure, that's lots of paid staff time wasted. But if they already had enough information to provide to the customer service to provide a summary to the customer, it shouldn't be that much harder to provide the raw info to ANAC. It may not be fully automated, but... At few hundred $ per claim, an existing semi-automated process would surely pay for itself if their objections were true, right?
It's likely way more complicated in practice, but I don't immediately buy the "it's cheaper not to fight it" idea, if the request is just for information they already have.
There is another possibility: because the first leg plane was late, it missed the pushback at 09:40 and then again 09:56 and the ATC put the plane at the end of the queue for takeoff until 10:48. ~~Though I can't imagine Lisbon to be such a busy airport to have an hour-long queue of departures, who knows.~~[1] In any case, if ATC denied takeoff/pushback because Air France missed the schedule, AF could not blame the ATC.
It's likely way more complicated in practice, but I don't immediately buy the "it's cheaper not to fight it" idea, if the request is just for information they already have.