I haven’t read the later two books, but my impression was that Pippi stories use somewhat similar device as some other Lindgren books like Brothers Lionheart and especially Mio My Mio, extremely unreliable narrator…and things like friendly cannibals in South Pacific should not be taken at face value. “Why don’t you have a father?” “I do, but he’s a king of cannibals in South Pacific and that’s why I live alone, I visited him just last summer…”

I have noticed children’s books tend to have quite strange role in cultures, there are books which everyone within said culture knows and can reference in adult books trusting people get the reference, but the same books can be virtually unknown outside that culture (there are several American children’s books I have come to know only through references in other books, for example anything by Dr Seuss…for quite a while I was puzzled about what this “Green Eggs and Ham” thing is).
Lindgren is pretty much the equivalent of Roald Dahl and Dr Seuss rolled into one, and really great writer (partly because she does put all kinds of weird undercurrents in her stories, so that at one reading you might get fun adventures and other reading of the same book can come off as an abandoned child making up a fantasy world.