I can't really answer that for GW, but I would turn a questioning eye towards the Wolf God Lupus, theorized to be the original God of the Cherusens, and His defeat and the usurpation of the canine sphere by Ulric, who is unquestionably a God of Humanity.
I did a bit of digging, starting by questioningly eyeing Lupus. Firstly, I think it's Lupos, not Lupus. Both appear in Tome of Salvation, but Lupos appears seven times and Lupus only once, leading me to believe 'Lupus' was a typo.
The word "dog" doesn't appear in Ulric's wiki page or anywhere relevant in Tome of Salvation. Beyond that, I can't recall off the top of my head Ulric having anything to do with dogs, only wolves. He's the guy who sends wolves to kill isolated peasants to toughen up their communities and such, not tame wolves into not-wolves. The only form of animal companions I remember associated with him are straight up wolves, like the ones Mathilde and Wolf met in Middenheim.
Archives of the Empire 3, the biggest source of lore on Rhya, implies she's responsible for the endoggening of the wolf. Belthani myths say she gave "domesticated grain" and tamed animals, and a contemporary myth says her handmaidens gave tame aurochs and secrets on how to tame the wild. Main problem here besides being 4e is that the first paragraph of this page (66) is entirely dedicated to talking about how unreliable all her lore is. That said, domestication and taming of animals is 100% within her purview, and she's old, so I think she's a more viable candidate than peasant-eating Ulric for who made dogs.
That all said, it makes perfect sense that Mathilde thought selective breeding was the origin of dogs instead of divine intervention. Her peasant upbringing would've first primed her with the usual Rhya myths, but since then she's gotten +5 Imperial Canines books. Books are written by scholars, and scholars are so urban they believe Rhya is a dead or dying deity, and so would've attributed the existence of dogs to secular causes. Mathilde's an academic herself, so she'd be biased to believe secular answers over the half-remembered myths she heard decades ago, and of course, Panoramia has an aversion to gods in general, so she'd grab for a secular answer too.