I was involved in rescue for years and can say with certainty that the overwhelming majority of organizations on Petfinder are nothing more than scams to solicit donations or individuals who hoard animals and use the listings as "proof" of "rescue" to claim a non-profit status for the tax breaks. With very few exceptions, the only reputable rescues on there are humane societies.
About 17 years ago, we contacted a rescue about a white German Shepherd, speaking to them in detail on the phone. We were led to believe it was all a matter of meeting the dog, then never heard back. Contacted them several times, with no word, until finally they told us the foster home decided to keep the dog. We were devastated, but, unfortunately, did go back to Petfinder over the years. EVERY SINGLE TIME, regardless of which "private rescue" we contacted, it was the same game. Either no response at all, and the dog would remain on the site for months, if not years on end, or we were given the runaround. I thought it might be different for cats, but now that we are looking for a kitten, it's the same old song and dance.
Honestly, Craigslist actually IS more reputable. I have worked with rescuers on there, transporting or fostering dogs, and know many people in my area who actually do rescue and rehome on their own dime placing dogs and cats through them. Just... stay away from Petfinder. It's the Ponzi scheme of the animal world.