If you read the comments again the airport spokesman says that the people in question had not even entered security 35 minutes before their flight was due to depart - remember that EZY's regulations require that passengers present themselves at the gate for boarding no less than 25 minutes before the stated departure time - so someone checking in on the deadline would technically only have 15 minutes to get up to security, pass through the security checks and then get to the gate - which can be some distance...
I agree with DWLPL that the problem on this particular day seems to have originated at the check-in stage...but no doubt we'll never know for certain as the LDP never seems to admit when it's got a story wrong....