It's not a question of owning all voices that sound like her, it's a question of "are customers deceived into thinking it is her" and "does it affect SJ negatively to be associated with this sound alike" when her income comes partly from her distinctive voice (much like Morgan Freeman). Sam Altman tweeting "Her" right before the announcements is what builds the case for SJ.
Imagine we hired a Leo Messi look alike and made him play football badly or something worse, if viewers can clearly tell it's not him it falls under parody but if we use camera trickery to keep a fooling doubt, we could be in legal trouble.