Well, maybe your family called for a bullshit emergency.

The wait times for actual life threatening emergencies are low. But the data is public, take a look for yourself. It's the same when somebody complains about long wait times in the ER. If they had to wait a long time, it wasn't an emergency. Simple as that.

Here is a video that explains it to non-medical people how it works

https://m.youtube.com/watch?v=Pyct1VyEMeE&pp=ygUfaGVsaW9zIG1hbmNoZXN0ZXIgdHJpYWdlIHN5c3RlbdIHCQl-CQGHKiGM7w%3D%3D

And here the data about ambulance wait times in the UK

https://www.nuffieldtrust.org.uk/resource/ambulance-response-times