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Sometimes you need to look a bit further than logical correctness. Yes the two sentences are logically equivalent:

"You cannot trust anything reported out of China" "Not all things reported out of China can be trusted"

But the language you choose to use has its emotional implication. Ask any Chinese, which of the two sentences is more biased.

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"