That doesn't explain why Miyamoto specifically hates lore though.
Interestingly, he's on record as having unironically approved of the "Super Mario Bros. Super Show" (at least the cartoon segments), which I think indicates where he's coming from on this. He's fine with using Mario characters from the main-line game series in just about any sort of lighthearted kiddy story, as long as it's a one-off.
In Japan there were three video episodes in a similar spirit where they did the fairy tales "Momotarou', "Issunboushi", and "Snow White" with the Super Mario 3 cast.