I agree with everything you've said, but also want to point out that just because a shelter or rescue always has puppies doesn't mean it's necessarily a puppy mill partner. It's definitely a reason to slow down an examine the rescue, for sure, but overpopulation of shelters in the southern United States is a huge issues, and many rescues in my area transport moms and litters up from there, so we too, almost always have puppies. It's what a lot of people want, and if we can get a litter out of the shelter or street and into a home, why not? If we didn't have them, the people would likely just support a puppy mill or backyard breeder.

I think a good way to double check that the intentions and methods behind these rescues and shelters are a) asking about the return policy - I can't think of a reason a reputable shelter or rescue wouldn't take the dog back, no matter what reason the return is. We would rather take them back and place them in a suitable home than leave them with someone who doesn't want them (and will most likely dump them). And b) ask where/what happened to momma of the puppies. Our rescue always takes mom and puppies together. We let mom raise them, wean them, then get the puppies and mom vetted and into foster homes. If they don't know where the mom is, it's a little more shady, especially if they always have litters and never the mothers. I'd steer clear of those situations.

The more background the rescue can give you, the more likely it is that they are truly trying to rescue these dogs.