You imply I wrote that with you in mind, but its really a WFTF rule. If I'm not mistaken, there IS a similar rule even for AAFTA matches.
While I didn't have your dog in mind, I DO know that in the past, there have been instances at local match where some doga HAVE run out onto the range due to lack of control by the owner (i never blame dog). I love dogs, and have owned many (you know I own one now).
The rule, in my interpretation, means dogs needs to be kept away from the competitors while they are shooting. They cannot run free at the shooting lines.
If this is a "deal-breaker" for you, I understand, and hope you do as well. I hope you understand that while some folks might be distracted by a dof in close proximity, the real worry for me is a dog being shot accidentally which would be miserable for us all.