That documentation may be wrong. On the other hand, it may be correct in the context of someone who is only using Arc, not Racket.
There are a lot of ways to conceive of what Arc "is" outside of the Racket implementations, but I think Arc implementations like Rainbow, Jarc, Arcueid, and so on tend to be inspired first by the rather small set of operations showcased in the tutorial and in arc.arc. (As the tutorial says, "The definitions in arc.arc are also an experiment in another way. They are the language spec.") Since #f isn't part of those, it's not something that an Arc implementation would necessarily focus on supporting, so there's a practical sense in which it's not a part of Arc our Arc code can rely on.
(Not that any other part of Arc is stable either.)