Dangers of non exclusive rights

Hello, I’m considering submitting a short story to an outlet this weekend but they only offer non exclusive rights. I’ve heard this can be good and bad but everything I’ve read is from non .gov websites. Thomas has mentioned in the podcast only to trust copyright information from .gov websites. I did look at copyright.gov but was quickly overwhelmed with the amount of information and technical terms.

Has anyone had a poor experience with non exclusive outlets?