It’s a poorly written article, but I think the concern is that after they infringe on our God-given freedom to decide what insurance to buy, and infringe on our right to privacy by getting the spawn-of-the-devil government improperly involved in providing our health care where they have no business being, the information thus extorted from us at gunpoint would then be fed into a database which BATFE is allowed to peruse freely, thus finding excuses to disqualify further thousands from gun posession. Anti-depressant use, suspected domestic violence, eyesight, etc. So they would be using one intrusion into things that are none of their business to enable another intrusion into things that are REALLY none of their business.
CDC made a declaration that gun storage is a public health issue and should be regulated from that perspective, I believe.