Interesting. My parents have no interest in moving out (they take advantage of many amenities and have formed friendships). I am using a caregiving service that my friend used for her mother for several years. It's considerably cheaper which is what made me ask the question in the OP.

My guess is that it's a list of providers they trust not to poach the residents.
A couple years ago, my parents were living in a facility, my dad was in the independent living and my mom was in the memory care unit. My dad wanted to hire a private care giver for my mom to come in for several hours a day, and another independent living resident recommended a small agency to my dad. It only took a couple months for the small agency owner to convince my dad to move himself and my mom out of the facility and into an apartment so they (small agency) could provide all the care. It was a super scammy set up and caused a lot of stress and drama for our family over the following year.

Anyway, I'd be less worried that any one was getting a "kick back" as long as the providers are good and reliable.

Agreed, will tip to supplement pay for good care.

No idea. I assume they will let you hire someone not on the list if you prefer? I look at this as a phase to just survive. You try out people, you enjoy it while it lasts if you find someone they truly like, but you have to be vigilant because sometimes the beloved care provider is the one telling sob stories for gifts. You also have to accept some parents will never be satisfied and if yours are lucky you! You try to make sure they have decent care, but you let go of perfectionism. If you have a good caregiver who seems to be honest, I would tip if allowed or give generous gift cards if allowed because it's so much harder to replace a caregiver they adore.

If an independent living facility provides a list of Recommended Care Providers for private duty, what are the odds the sales department gets a kickback from anyone chosen?

Not sure how much I am to value being given this list of names.