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Apparently, this should be considered a valid story, as there are likely several versions of it – and perhaps even all of them are true.
In short, let's go through it in order. The station attendant has nothing to do with trains; those who remember Pushkin will recall that we are talking about a station where horses are changed, and yes, they existed in Europe as well.
Once, after a major international chess tournament, Andersen was returning home – not as a world champion, because that concept didn't exist yet, but if it had, he would have been one of the main contenders. He had to wait for the horses for some time, so the station attendant suggested a game. Andersen decided, in modern terms, to troll and said that he didn't know how to play. The rest is clear: after receiving a handicap in the form of a queen, he deliberately played poorly and lost. Then he suggested switching roles and played at full strength, easily defeating the amateur. Until the amateur had a breakdown.
I would consider the chess tournament version to be valid, but since there is a similar story about Lasker, perhaps Hermit answered correctly; I will just ask for confirmation.
For example, about Andersen, see: Panov, The First Book of Chess, 1964.