There are two ways of looking at this problem.
One is, White Glove bans animals and if you are going to disregard this and carry an animal who else and what else will you lie about? It is a simple case of honor when you say you do not have an animal in your truck don't have one.
As far as the insurance goes in the surface world we have no problems having Molly our Cocker Spaniel with us. Molly is well know at FedEx Custom Critical head quarters. Times are changing though and with a dog you can now get your DoD clearances. So far we have only been to one nuclear power plant that did not want animals or passengers in the truck when you went on site. Only the driver of the truck permitted inside. We have been to several bases and have also had no problem with Molly and in many instances I believe she has helped us a ambassador of good will!
So our thoughts are if you are in White Glove and you have an animal shame on you. Don't forget also that if caught with an animal it is grounds to have you lease terminated.