Recently in a different context I was presented with something like this:
[When something big happens], you'll see them all run for cover.
At first I thought this was very idiomatic, but when I looked at the well known idioms I couldn't find exactly run for cover(sure it's about running to the place of safety, but isn't that place usually not the shelter more than the cover?) - what I found was take cover, run for it/for one's life and try to cover one's ass.
Do the idioms compete or interfere with what is being said here? Does the native speaker get a mishmash of two or more idioms or just the literal meaning because it's neither exactly? Are there any negative connotations in the provided example - does "all" provide any clue into that; is any context obvious, such as that of the fleeing civilians, or the business management setting?