Yes, someone who's come into a large amount of money to make an unusually large credit card payment could have done so illegally, but said someone, Mr. Hypothetical Terra-ist Sympathiser, wouldn't then turn around and spend that money paying off their credit card, would they? Not to mention the sheer creepy factor of the government watching and intervening in that and not doing any of those silly things like telling the person in question where their money went, or showing up on their steps to ask them some questions, since they're such a dire threat, after all. Clearly they just need to have their money silently freeze while the ponderous wheels of government investigate the matter.
At least it's not my government.