It would seem odd that a pokemon known primarily for spinning leeks and tasting delicious would be the source of the term "Far fetched" (or "Farfetch'd" as many grammar purists insist), but given the stories which have sprung up around it, it is not as bizarre as it appears.
Some of them are fairly sensible and plausible, if always heard from a friend of a friend and never quite true. The restaurant which secretly domesticated the notoriously untameable Farfetch'd is in reality serving Psyduck meat, the magic leek which doubles their attack power is real, although their defenses and speed remain so poor that a trainer would be lucky to make the Pokemon League with them, let alone win it like they claimed.
And then there are the stories which are more out there. The President of Unova has had to deny rumors that his father was a Farfetch'd spread by his political opponents, and it speaks to the absurdity of politics in that region that the rumors even started. Likewise, the girl in the popular "leek spin" internet meme is not secretly a slave of a Farfetch'd colony in the Sevii Islands, and the idea that global warming is really caused by a pokemon which is neither fire nor ice type is too silly to even bother refuting.
Despite the obvious ridiculousness of these ideas, Farfetch'd continue to be a magnet for strange tales. I urge any readers of this pokedex not to spread these ridiculous rumors, and to be careful to source any information about Farfetch'd they discover before believing it or passing it on.