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Morton's fork is the term given to a tricky bit of sophistry in which contradictory evidence is used to draw the same conclusion. It is named after Cardinal John Morton (Henry VII of England's sidekick). Morton went around England "persuading" people to give money to the government. If they were lavish in their spending it was proof they were rich and could afford to pay what was asked, if they were less forthcoming, it was evidence that they must have a great dealing of savings from living such an austere lifestyle, and hence could likewise afford to pay.
Variations of this are often used by creationists, who will use any observation, as well as its inverse, as "proof" of Biblical literalism. This is also a favorite of conspiracy theorists, who believe evidence against the conspiracy is actually evidence for the conspiracy because those perpetrating the conspiracy are obviously covering up the necessary evidence.
This fallacy can be neatly summed up by the phrase "Heads, I win; Tails, you lose."