Yes, you have to lie to them about that or you will not be able to rescue a dog and give it a decent life, they are fucking bat shit crazy in some of these places.Before I got my dog I went to a lot of shelters, none of them would let me have a dog because I work a regular hours job and thought it was wrong leaving a dog at home while I work, not sure how that's worse than one being in a cage with no love for 23 hours a day but anyhow..... Staffies of all the dogs seemed to get what was going on, they were absolutely desperate for someone to take them. Really bright and lovely dogs, sadly with a bad rep because of a few bad owners.
I rescued ours from the Dogs Trust in Liverpool (of all places) we went to see the dog on the Saturday, all the way from Carlisle but obviously they wouldn't let us take him home that day but if our home passed an inspection we could take him the following weekend, I said it is a 4 hour round trip and I am working the following Saturday but nope.
Got a phone call on the Monday saying they couldn't send anybody up to view the house so could we do a video of the house and garden.
I was in the middle of rescaping the garden so it was like a builders yard, I had to move everything around the garden while she stopped and started the video until she got a panoramic view of it looking clean and spotless.
For the next week, I was working in the dark after work laying 4-5 ton of slate chippings before the dog arrived.
But they asked us if we worked full time, I said I did but the wife was a stay at home wife and they were fine with that but she works part time and the dog has never batted an eyelid in 3 years about it.
As you said a loving home or a cage and possibly being put down.