The point of the joke (and the point of most other jokes so far in that comic) was to take an usual event in pokemon, but suddenly bring it to a more realistic, real-life context. The "main character" representing the fictious side of the story, the one people who play the videogames are familliar with; the more snarky main character represents an unexpected, out-of-context realistic light on each events. You could say this snarky character represents a reader of the comic which fails to have suspension of disbelief regarding the story, pointing out things that "dont make sense", even though it seems to make sense to every other character in the fictious universe.
Choosing to make the latter call animal rights was in order to make an out-of-place pop culture reference: real-life animal rights companies like peta obviously not existing in the Pokemon games or shows (or at least not in this form). Making them call officer Jenny instead of unexistant peta-like organisms would thus ruin the joke, as the whole basis of the comic's humor is to compare the pokemon fiction with reality.
