Please don't lump all of the rescues together under a couple of generalizations. VGSR has tried very hard to hit a good "medium" between too strict and too lax.
In our own rescue, I like to see fences (if a homeowner) and yes, we got burnt by adopting dogs to people with toddlers.
So we like "over 8yrs. of age" on kids, and fenced yards if you own your own house.
Yet tomorrow, we'll be adopting a little dog to a home with a 3-4 yr. old toddler and no fence.
To the OP, do you know if the 6' fence is a strict requirement yet, or have you contacted them? If a good owner was to contact us and say "our fence is 4'" or whatever, I'd still look at the overall picture.
We had a woman apply a while back with a fenced yard and all but amazingly her kids leave gates open and their last few dogs had been ran over when that happened. Fenced yard or not, they hadn't addressed that issue so we didn't give them a dog
So, basically, as a rescue, we look at the entire picture. If your last few dogs lived to a ripe old age of 15 with no fence, you're more likely to get a dog from us than if you don't have a fence and the last few dogs were run over when a gate was left open, or stolen while you were at work and left the dog out all day.