Sometimes rehoming groups work with other smaller rescue organisations to save dogs, and these are often dogs that are found as strays. Quite a few dogs in English rescue centres are from Ireland, just because England has a lot higher population, therefore more people looking to rehome dogs. Others specialise in rehoming Romanian, etc strays.
So, a lot rescue dogs' histories are vague - our chap was found as a stray in Ireland, emaciated and matted. The Dogs Trust helped him recover, and put him up for rehoming.
They were fully open about the fact that his past was a mystery - that he seemed very friendly, and house trained. He was also neutered when they found him, and we realised he understood basic commands (sit, paw) so it was obvious he'd been in a home that cared to some degree. He's lovely with children.
We've had him for nearly 11 years now, and I do still occasionally wonder what his story was (especially as he's a fancy crossbreed). Was he stolen, then let loose by the thieves? Did he do a runner and his first family couldn't find him (his recall was terrible when he was younger, if he saw or smelled something interesting he'd just sprint)?
Some smaller rescues aren't dodgy, but they might be a bit overly relaxed about potential issues with a dog, or haven't correctly identified a dog's needs. My in-laws took in a rescue who was supposed to be good with other dogs, and she was a tiny murder beast to their two terriers. Turned out she was only OK with dogs bigger than her, and sadly they had to send her back, for the well being of their other two dogs.
Don't be afraid to ask questions about the dog's behaviour - how are they around children, other dogs, cats, etc, have they ever shown signs of aggression to people, etc. A good rescue will be glad you're asking questions, and honest with questions they're not sure of the answer to.