She didn't give up she just eventually figured it out, he doesn't have any pets, he was just havin a laugh. The semi-explanatory middle column from the dogs in apartment emails:
Well I figured there must have been something that the neighbours had complained about. That woman wouldn't just email David and ask if he had any pets in his apartment.
I want to meet David Thorne, I'd buy him a few drinks of whatever it is that they chug in Aus. I have the spider conversation as a big poster on my wall and a giant ASCII art spider next to it.