see also https://en.wikipedia.org/wiki/Cube_root#Complex_numbers

I don't think they are intending to cast aspersions on the validity of taking a cube root of a -ve Real number.
They even state "For real numbers, we can define a unique cube root of all real numbers.".
They follow that immediately with "If this definition is used, the cube root of a negative number is a negative number."
That wording is a bit odd, but I don't think they're suggesting that there's some alternative stance to take wrt cube roots of -ve Real numbers in the *Real* field.
Rather, I think they're acknowledging that this definition is deficient in the Complex field (even for -ve Real numbers in the Complex field) because, in the *Complex* field, the relationship between a -ve Real and its cube root is no longer one-to-one. It's one-to-three.

Cheers,
Rob