I agree that being the first is important.
I have had a paper reviewed, then rejected, only to see the same idea elsewhere a while after. I cannot say the reviewer "had the same idea" nor prove, but it is known to happen. Putting into arXiv remediates that.
However, my personal issue with that is that the journal might not be that keen to want to publish your paper after knowing it was publicly available elsewhere, as they thrive "innovation" and "being the first" as well.
It's a very difficult problem, indeed.
What we did in the past was contact the editor first and ask if they have any problem with it being pre-published. Some do (most of them in our experience), some don't. The paper always change between arXiv and the journal, so the source of truth is the journal.
> I have had a paper reviewed, then rejected, only to see the same idea elsewhere a while after
I've seen worse. A grant being rejected by the grant reviewer, only to be re-submitted slightly changed by a reviewer's friend (this is a small world, we know each other) the next year. The inners of science suck, most of us keep doing it because we are like monks: we love God (Science), but we hate the Church.
