As true as that is, jealousy can actually be considered an illness that makes people suffer paranoia. They might think there girlfriend nipping to the shop to get some bread is them nipping out to chat-up the shop assistant.
They over-exaggerate things and remember things from the past (Such as when she walked past her Ex from 3-years ago) as sad as it sounds, it's not easy. I have knowing people that have bad jealousy and it ruins relationships, the girlfriend feels trapped and doesn't know what to do.. things can end up controlling even.
I'm not accusing this guy, my only advice would be if you and her were serious about each other try and fix things, if she thinks you were too jealous then let her hang with her friends and turn your phone off for the night. Don't be worried, let this be a lesson. You can either lose her and watch her be happy with someone else due to you being jealous, or don't be jealous and have her.. instead think about how shes not going to run off with someone else and about how shes yours.