I mentioned the following scenario a couple of posts ago. I will now expand...
One clear, calm November morning, sometime in the mid 1980s, Sean McMinn and myself were birding the fields to the east of Boulderwall farm at Dungeness. It was a glorious morning, a real pleasure to be out. We picked up a small, dumpy passerine high above us and it called once. It was a dead ringer for a Trumpeter Finch. Sean was familiar with them from many visits to the Middle East. The bird carried on eastwards and out of view. It did not call again.The air was still, the acoustics were excellent, and we both felt as if a star prize had got away. We didn't release the information and only mentioned it in passing to our close birding chums.
The only other time that I have (knowingly) recorded a rarity but not submitted it was also in the company of Sean. It was late October and we were sitting in the Dungeness Bird Observatory back garden, mugs of tea in hand. We didn't see the bird that called, but it was very close - without doubt a Red-throated Pipit. We had both seen (and heard) hundreds in Israel the previous year. It did not call again. We decided that there would be little point in submitting it, or even mentioning it.
The more time that you spend in the field, the more likely it is that such incidents will occur. Dealing with them can be interesting.