While that is true, it may only show an icon for pets if all the hotels in that zone at that star level take pets.
I stay in one area on a regular basis, bidding on a 3 1/2 star hotel. There are two hotels they use, one allows pets and one does not. They do not show the pet icon in that case because not every hotel you may get accepts pets.
And again, just because they accept pets doesn't mean it won't cost you more than you paid for the room or they will accept your pet.
I think it's just too risky to bid blindly on a hotel unless you are certain which one you will get and what their policy for pets is.