Really depends on either how serious a runner you are or how serious you take yourself.
Nothing wrong with considering splits or self timed runs as a PB or even using GPS as a basis. Taking a corner off the race line can add a fair distance to the race so accuracy is relative anyway. Very few people adding to this forum are going to need to worry about the extremes of accuracy. Some people choose never to run races and their personal best is just as valid as anyone else.
Having said that if my 5k PB was part of a 10k run I would be pee'd off with myself and would need a new 5k PB as soon as possible.
@ The the real Mr I. If you applied your test to every topic of discussion I am sure you would say very little or be very boring to your friends due to your need to discuss only matter of great importance.
@ the OP. Yes it is weird to buy a random medal but you are making a bit of an adventure around it. If I were you I would start tracking down the medals of other long forgotten races and then make a series of it. Or maybe (going in a different direction) buy an early 90's london marathon medal and run the original route dressed in a shell suit / acid happy face tshirt.
Let us know how it goes. It could even be one of the few running blogs that would be interesting.