It isn't about you being a more responsible or better owner. Don't think that rescue people think you are a bad owner if you don't have a fence. They don't, I assure you.
Adoption isn't about you, it's about the dog that they are trying to place at any given moment. Rescues can and sometimes do make exceptions for certain dogs, but it's on an individual basis according to the dog's needs.
We get many really wonderful people applying for dogs, but we match each dog by it's needs to the best possible conditions. So if there is a situation that is more desirable than what you are offering (in this case a fenced yard), another potential adopter(s) is going to be considered over you. So if there is a waiting list of people with fences, and then there's you...
If the dog has certain emotional, medical or behavior modification needs, we may require that the potential adopter is home for the better portion of the day. If the dog is crippled, we may require a ramp if there are steps. If the dog is unruly or maybe rough with kids, we may have age restrictions on children. But it's by individual dog. Foster homes live with these dogs and each dog is assessed according to his skill level, temperament, health, etc. We try hard to find out everything we can about each dog long before he is put up on some website for adoption. But we can't know everything and have to assume certain things. Like if the dog might be a squirrel chasing, door bolter who can slip past a sumo wrestler in a nanosecond and run into the street before the owner knows what happened.
Some adopters are hoping for a dog that would do well in therapy, some want to do water or draft work, some just want a companion. We take all those factors into consideration as well and if we don't have a dog that meets that person's requirements, we will keep them in mind for a future rescue dog. But we won't give them a dog that isn't suited to them or whose own needs can't be met, just because they are wonderful responsible owners. And we don't choose the application that is at the top of the waiting list. It has to be the right match.
Rescue doesn't have an unlimited supply of dogs, and nearly all of the ones they have, came in with some kind of issue. We never have any healthy, perfect temperament, well trained dogs waiting in queues for homes. It's a lot different than homing a puppy who is a blank slate.
If you want rescue to reconsider you, ask if someone will come to your home, observe the conditions, meet all the family members, see your own dogs, or make suggestions, etc. If they are satisfied, then ask them to keep you on their list for a future dog that may be better suited to you.
That being said, some rescues are adamant about things like fences. It still doesn't mean they think less of you, so please stop being offended if you're turned down. It isn't about you.