Hi there, that would be correct. If the cat has been missing/off the region for more than 3 days before a support ticket is filed, then the cat will be returned sick. Usually tickets are filed within a day of cats getting lost and they are returned healthy. It is also possible that the cats are sitting in your inventory for a few days after the Support Team sends the new copy to you, which the cat would not have access to kibble in there and will get sick before being set back out in world.
I hope this information helps. If you have any questions, please feel free to contact me in world or file a support ticket and the team will get back to you with more information