XOR of one-way function
There are two reasons that counter-example wouldn't "imply that we've inverted".



(a)

Despite that answer's (probably-not-necessarily-correct) opening sentence,

it's only a counterexample to "$h$ is necessarily one-way", not to "$h$ is one-way".

(b)

That answer's attack does not require inverting ​ $\hspace{.04 in}f(x_1) \oplus f(x_2)$ ​ "to $x_1x_2$",

it just involves finding a preimage of ​ $\hspace{.04 in}f(x_1) \oplus f(x_2)$ ​ under $h$.