“That was certainly the case some years ago. I bought a handgun and rifle at once, and the dealer informed me that because more than one gun was purchased, he had to report it to the BATFE.’
The dealer may have thought it was the law. That does not mean that it was the law.
The "day job" of the dealer I was working with is "research librarian". I doubt that he would be mistaken about what the rules were. And more than "just me" on this thread recalls such notification as being required.
What do you base your opinion on?? Are you a dealer??