Can't say what others do, but....
When I don't sign the log, I don't log the find!
If timing is important, (and it must be important to both of you or you would not be discussing who was first), then there has to be a standard for determining who was first. Clearly, signing the log is the only reliable way standard.
One time, I climbed to the top of a mountain and waited and waited for some artsy type photographer to leave. Just when I thought they would leave, out came lunch! Not even 20 feet from the cache. Posted a DNF (or note?). A few weeks later, i went back and, of course, had no trouble "finding" it.
On another cache, I was able to see the cache, but had to walk another mile before I could actually touch it! Seeing it was certainly not finding it!
The way I look at it, if it's worth finding, it's worth doing right and worth going back again!