No Invisible Fencing for containment:
This organizations founders setup the invisible fencing policy for several reasons.  99% of Great Pyrenees do not respect the fence
We have gotten in dogs that were burned and had sores from the collars. 
A lot of the dogs in rescue are strays or runaways that the owners no longer want to deal with. Some are failed Livestock Guardian Dogs who would not stay with the flock in a fenced field.
The second  is that it does not protect people or animals who may wander into your yard.  The Great Pyrenees are guardian dogs.  Invisible fencing gives people the false sense that the dog is friendly with everyone because he is not in a fence yard. It looks like he is free in the yard thus trustworthy.  
The third reason reason we do not allow this is because it does not protect your dog from intruders or other animals.Your dog could be attacked and can not get away. It is trapped in that area.  It is not a deterrent if someone wants to steal the dog like a fence is.  Off comes the collar and there goes the dog. 
We once had a dog being surrender at 10 years of age because he nipped the delivery man.  Even though the signs in the yard told the delivery man to put packages in the plastic shed outside the invisible fence area he ignored it and came running up to the porch. They were  being sued because the dog nipped him.  Their insurance was talking about cancelling them .  No insurance means their mortgage was at risk of being called in. Their only options were surrender or put him down. For doing what he was bred to do, so wrong and cruel.
This organization stands behind its policy.