when you open a dead persons eyes do they stay closed?!

A buddy I work with works as an EMT and he was telling us about a person he was called out to up recently. She when they got there the lady who said she found the guy said she found him not breathing and it was the first thing she noticed. However she says when they got there the guy's eyes were open. She says they asked her if she opened his eyes she said yes she wanted to check his pupils. She told me she did not believe her because if you open a dead or unconscious persons eyes they always close again. Is that true?