I personally think that this article is short on fact. I can only recall one case where the ATF went into a gunshop in Arizona and asked to get copies of the Forms 4473 from a new employee. More experienced people at the gun store told the ATF to go get effed. They may ask, for now, but it is illegal and the gun seller does not have to comply unless there is a specific warrant on a sale made for a specific gun.
I hope you are right. I read the line you quoted and seriously could not envision any dealer I use allowing access to the 4473s in their possession. If you and I are wrong then we are very much screwed.