It is true the rents are really high right now. And having pets complicates things and narrows the potential rental pool considerably. It is true it is also cheaper to buy - but only if you plan to stay in one spot for a few years. Or get an incredible deal.
I help people with both rentals and buying, and green is my niche. I just helped a couple find a place for a move from Phoenix to here. I have also managed to talk "no pets" landlords into taking pets before, with a reference letter from the current landlord. The right approach pays off.