Not true.
Companies file quarterly returns with the IRS directly and the Social Security Administration directly, usually accompanied by a wire transfer, but sometimes a check, depending upon the size of the company reporting.
The states are not, and never have been, intermediaries in this process.
I agree with that, maybe it is time the states take a more active roll in trimming back the Fed. I'm trying to find the link (read it here on FR) where Missouri was (at the state level) looking to enact such an idea (which is where I got it from).