I don't even care whether that's true or not because it's so misleading. The 'carbon footprint' of a dog is fast-cycled carbon that comes from photosynthesis a few years ago (eaten by some herbivore then passed through the food chain to the dog). It was carbon taken out of the atmosphere just a few years ago. It's ultimately environmentally neutral, the carbon excreted by the dog is no more than the carbon taken up by the plant at the beginning of the cycle (obvious, right?), and it will go back into another plant.
The carbon from an SUV has been sequestered for hundreds of million years, and the carbon sinks do not exist to take it back up quickly. The carbon it excretes is not environmentally neutral.
"Now we have to feel guilty for owning a dog?"
No, but whoever wrote that article should feel ashamed for being a dishonest bastard, and you might should feel embarrassed for falling for it.
That would be true if the SUV were using biofuels or renewable energy. I can believe a great dane or Mastiff would if they were fed meat that was raised industrially. A miniature dog, no.
feeling guilt is a non issue as it is a time relative issue...the real issue is what is your contribution to the carbon footprint and what are you prepared to do about it...vote with your own actions and your own use of your own disposable dollar, instead of looking for "rationale" excuses that increase debate and do nothing but contribute more to trivial pursuits.