Why would $1^{-\infty}$ not be 1?

Since for any $x$ we have $1^x=1$ as you noticed

$$\lim_{x\to -\infty} 1^x =\lim_{x\to -\infty} 1=1$$

and you are completely right on that, but as $f(x)\to 1$

$$\lim_{x\to -\infty} \left(f(x)\right)^x $$

is an indeterminate form, that is we can obtain any result depending on the nature of $f(x)$.

Probably by this input wolfram refer symbolically to this latter case.