In his Notes on hiring a copyeditor for CEA, Aaron writes:
... I’ve also kept a record of the other applicants who most impressed me, so that I can let them know if I hear about promising opportunities. I’ve already referred a few candidates for different part-time roles at other EA orgs, and I anticipate more chances to come.
On Rejection
I'd be quite surprised if rejection were frequent. I've been part of / close to a few organizations and haven't heard it discussed. A few reasons:
I think (2) is a pretty good reason, for humility reasons if nothing else. Applicants may have a lot of good reasons for doing things that may at first seem sub-optimal. (3) is also pretty good. I could imagine instances where there's one highly-anxiety-producing but seemingly-effective option for a person. It seems kind of cruel if all their other job prospects refuse them to force them into that position. I could imagine some pretty nasty decision consequences that could result if that were a consideration.
On Recommendations to Other Orgs
I have witnessed cases of organizations suggesting good people to other organizations, especially if they both (1) think they were good, but (2) didn't fit with their own application process. This seems pretty reasonable to me.
Personally, when I chat to potential hires of things I'm working around, I try to be as honest as possible regarding to which organizations they would be best for, even sometimes connecting them with people representing other organizations.
In some sense these organisations are competing, but in a bigger sense, we're all trying to help make sure the world goes OK.