How can I verify if an airline is telling the truth about the reason for the flight's delay, in the context of EU delay compensation?

Today I've received the following email from Air France in regards to my request for compensation under EU flight delay rules:
We are really sorry to learn our flight AF379 delay on 15th August 2018 disrupted your travel plans. We understand that delays inconvenience our passengers, so we do all we can to limit them. However, we sometimes face extraordinary circumstances when Air Traffic Control delays a flight’s departure or arrival. These Air Traffic Control delays are beyond our control.
As you may be aware, compensation is laid down and paid in accordance with the EC regulation 261/2004. In line with this regulation - and our General Conditions of Carriage - I must respectfully decline your request for compensation on this occasion. I am sorry for any disappointment this may cause.
How can I verify if ATC is in fact the cause for the delay of my flight?
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Are airlines required to compensate for delays?
There are no federal laws requiring airlines to provide passengers with money or other compensation when their flights are delayed. Each airline has its own policies about what it will do for delayed passengers. If your flight is experiencing a long delay, ask airline staff if they will pay for meals or a hotel room.How can I prove my flight is delayed?
However, you'll also need:What the reasons for airline delays are?
The most common reasons for flight delays- Air Traffic Control (ATC) restrictions. ...
- Adverse weather conditions. ...
- Bird strikes. ...
- Knock-on effect due to a delayed aircraft. ...
- Strikes. ...
- Waiting for connecting passengers. ...
- Waiting for connecting bags. ...
- Waiting for cargo.
How long can a flight be delayed Europe?
Compensation when re-routedType of flightDelayFlights of 1500km or lessmore than 2 hoursFlights of over 1,500 km within the EU and other flights between 1,500 and 3,500 km3 hours or lessFlights of over 1,500 km within the EU and other flights between 1,500 and 3,500 kmmore than 3 hoursAll other flights4 hours or less2 more rows•Feb 28, 2022Flight SECRETS Airlines DON'T Want You To Know
Sources: Stack Exchange - This article follows the attribution requirements of Stack Exchange and is licensed under CC BY-SA 3.0.
Images: Enoch Patro, Gustavo Fring, Andrea Piacquadio, Andrea Piacquadio