Nitpick, but those 2 sentences are not logically equivalent: "You cannot trust anything reported out of China" = "Nothing reported out of China can be trusted"

Nitpick, but those 2 sentences are not logically equivalent: "You cannot trust anything reported out of China" = "Nothing reported out of China can be trusted", while "You cannot trust something reported out of China" = "Not all things reported out of China can be trusted"