hmmm i think a lot of that site is scaremongering...
my family has always kept many kinds of animals together and never had an accident.. i even had a wild tiel that had a broken wing once, i kept it in a small aviary on the verandah and cared for it till it got better and flew away.. the cage was always open, and we had 3 farm cats, a jack Russell terrier and numerous border collies we used to breed.... all of which were well fed, well exercised and had lots of attention-the most important part..
i agree that a well fed cat is less likely to hunt, and that you should be cautious having birds and other animals around together, but to that extreme?
my tiel loves my eldest dog, she even preens him... and is healthy!
my dog is well trained, but i know of few people willing to give up as much time, effort and money as i did to get a dog who is able to be trusted around small children and small animals alike...
he is almost 8 years old and will not retaliate to violence from anything small (children, cats, birds, small dogs, ferrets) when such an attack happens, he comes to me and is trained to jump op on to my shoulders... he is a big dog, but knows just the right way to stand, distributing his weight evenly...
i once had a shocked parent watch as her 2 year old ran up to my dog in a park and punched him square in the nose, to which Garm yelped and jumped into my arms...
i guess my point is, take care, but just remember its the owner who makes it work with a lot of effort (possibly unending) and the knowledge to realise when you should trust or not trust!