They are not trying to screw the system, and aren't even claiming for the cost of the flights on a different carrier they used because EZ were going to leave them there for another 2 weeks.
Funnily enough friends with 2 young school kids stuck in Spain recently because of ATC cancelled flight, then rebooked on flights for strike day and then told they could get a flight on Oct 5th as earliest day, got told by call centre they could book flights with another airline and Easyjet would pay which they did but now Easyjet telling them that was never said to them and they £1000 out.
I have suggested requesting a transcript of call but not hopeful for them and trust me they struggled enough to get to family wedding.