Because Fox.
HRC was a cabinet officer: nominated by the president, confirmed by the senate. All such appointees are “political appointees”, not employees. Employees have employment rights; political appointees, per the Constitution, are only in office at “the pleasure of the president”.
The form Fox is on about is known to anyone who’s been an EMPLOYEE of a federal government agency or department. There are millions of such employees, and more millions of such ex-employees. There are also, at any given time in Washington, thousands of former political appointees and former elected official, mostly now working in lobbying concerns and so-called think tanks. Many of those former political appointees and elected officials, to say nothing of thousands of former employees now working in more politicized positions in and around WDC, would be familiar with the concept of an employment separation form.
Let’s say I was at one time an employee of a federal agency (which, I was). Assume I spent, say, a couple of years working as employee with a federal agency, then left, yet continued to work after leaving on a contract or case-by-case basis. I’d sign an employee separation form when I left permanent employment, but I’d not be called up to sign such a form as a contract worker - even tho I could be working out of the same physical location on the same sorts of issues. But I would be bound by the terms of the contract I worked under and any related secrecy oaths, both general and specific, whether administered orally or, as is more common, in writing (There are a large number of federal laws and regulations that reference the specific requirement of an oath.), and the commitments associated with those oaths would, on their terms, NOT end upon the contract work ending.
Next, assume time went by, as well as a few administrations, and eventually I was appointed directly into a position within a federal agency, where I stayed for a few years before moving on to another federal agency and moving around among jobs in the latter. As an appointee, I would be bound by the same sorts of oaths that bind some employees and contractors, and more, and so I would NOT be called upon to have to sign a separation form on leaving that position. That would be not only because I was not serving as an “employee” during the periods I was serving in those agencies by appointment, but also because I would be bound by the general oath administered on assuming each position, plus any other additional oaths, whether administered orally or in writing, as called upon. And THOSE oaths would extend even further, in terms of each of information and over time, than either employment or contract.