I wasn't trying to catch anyone, just clarify the point. It is a signoff in that BATF will not approve the sale without it (except to a corporation), it just isn't a "permit" or an "approval", at least it isn't supposed to be. One CLEO (in another state) told the press that he never signed Form 4's because if the buyer "went and shot somebody with his machinegun they could sue me for letting him have it." That was his excuse for not doing what he wouldn't do anyway. The same excuse is often used for denial of handgun purchases or carry permits.
(In Maryland, the only recognized CLEO is the State Police, who also approve handgun sales; they are immune by law from any civil action over approval of gun sales as long as they stick to the law. I know of no Form 4 being rejected by the MSP. Better than a patchwork of local chiefs and sheriffs.)