Do cats poop outside the litter box if they're upset?

We have two male cats and they get along and have lived here for 10 years. Both cats like to hang out in the bathroom, I assume because people go in there. One cat spends a lot of time in there and will sleep on the rug or just hang out.
When I got home today bathroom cat was sleeping on the bed and other cat was running around. He gets excited when I get home and likes to run around. I split time giving each attention. Eventually bathroom cat got up and started wandering about. Fast forward an hour. My wife gets home and goes in the bathroom and lo and behold, one of the cats has pooped all over the rug. This happened once before when one of the boys had some loose bowels, but this was solid poop, albeit a bit soft.
I don't know which one did it. Both are seemingly healthy and happy. They get lots of attention and play. Would a cat poop on the rug because of territory or jealousy? It is a bit upsetting.