Falsely Claim

I've noticed in some political stories that the writer will say that whoever they are denigrating has 'falsely claimed' so and so. I'm not a grammar Nazi, though I will pretend to be one when it suits me, but this phrase just strikes me as off. You can make a statement claiming most anything. What you are claiming may be true or false and so the claim may be true or false, but 'falsely' is an adverb modifying the verb 'claim', it is not modifying the contents of the claim. 'Falsely claiming' must mean you are not really claiming anything at all. It's like not saying anything. The phrase 'falsely claiming' is a wrong and stupid. Don't use it.