The range of stupid and thoughtless comments that government public affairs workers can make is pretty unlimited, so there’s no way to verify that one of them could not have written such a slap-in-the-face letter. But the spotty record now available strongly suggests that if any of them had, it would have been out of step with standard NASA advice even in the early 1960s.
It’s also possible there was such a letter and it was ambiguous and misremembered. “No girls allowed” might have reflected the same thought in one of the remaining letters, that children would not be accepted.
Another piece of evidence related to the existence of such a NASA letter is in negative form. With thousands of people writing to NASA about becoming astronauts in the 1961–2 period, and presumably many of them being females, not one other written example of an official “we-don't-take-girls” put-down response has ever surfaced, to the best of my knowledge and that of other space historians with whom I’ve conferred.
It's not just a question of nobody, forty years later, recalling getting such a letter and then, long afterwards, going public with corroboration of Clinton’s highly-publicized story. The issue of women as astronauts was a hot topic in the American news media at the time (1962–3, especially after Tereshkova's flight), with major newspaper and magazine coverage of medical screenings and of Congressional hearings. NASA was being lambasted for not taking women into the current astronaut corps.
It defies the imagination—at least, my imagination—to require that dozens or more of we-don’t-take-girls letters (assuming that such was the standard NASA response) were out there in the hands of disappointed and angry young aspiring female space fliers, and not a single one of these misogynistic missives got into the hands of some journalist or campaigner or politician to fuel the ongoing public debate and embarrass NASA. Yet in all the public debate, which I personally followed as a teenager and then more recently researched in hindsight in archives, both hardcopy and Internet, did I come across any “smoking gun” of NASA’s proclaiming girls should not dream of flying in space.
Instead, the official advisories seemed to describe current selection standards as they existed for current reasons, that were subject to change as technology evolved, And had Sally Ride (or any of her fellow female candidates) written such an inquiry to NASA in that period, the answer would not have been “no” but “not yet,” along with advice, “do what you can to prepare yourself for that time.” And many of them did exactly that.
Whatever young women were being told in such letters, the realities were catching up with their aspirations. The US was moving towards genuine gender neutrality in astronaut selection, even as Russia—trapped in its gimmicky lone-stunt approach—has even now failed to reach it.