A passenger telephoned ATC at Heathrow complaining that his flight had been involved in a terrifying near miss and he wanted full details in order to take the matter further. It came as a surprise to us as nothing untoward had occurred. When the gentleman was advised that we were not aware of any problems he claimed that we were "covering up", took my name and said he would send a full report to the appropriate authorities.
The matter was investigated and we came to the conclusion that his flight had turned in the holding pattern at the same time as one above whose track was slightly outside his aircraft. Hence, when the wings were aligned in the same plane there was only around 1000 feet "horizontal" between the two aircraft. I've experienced this myself but luckily I knew what was happening. Presents great photographic opportunities though.
Moral: Trust the people up-front; they know what they're at and the ATC service is reasonably competent too. Well it is now I've gone!