Comfort items are welcome. The advice is about choosing the item, not about avoiding it.
What the agreement says
Clause 4 of the boarding agreement says you may bring comfort items. It adds that each kennel has a cot, air conditioning, heat and blankets supplied, and that the kennel is not responsible for bedding or toys that are damaged, destroyed or lost. Dogs play hard in a run, and a soft toy can be chewed apart in an afternoon.
Picking the toy
Choose one toy you would not mind replacing. A familiar smell helps a dog settle, but the one he sleeps with every night is the one to leave home. Mark it with your pet's name, because the kennel asks that all belongings be labeled. Leashes, bowls and balls are provided, so there is no need to pack those.
What is already in the run
Every run has Kuranda raised beds and plenty of blankets, and heat and air conditioning keep the temperature steady. The kennel does not recommend your own bed, because the supplied bedding and the climate control cover it. The packing list is short, and a slow-feeder bowl is the main extra for dogs who use one.
Collecting belongings
Staff carry belongings to and from your car. When you pick up, check that everything you brought is in the bag. If something looks missing, mention it before you leave. The toy guide lists tougher choices, and the packing list prints on one page.