That's called commercial bribery and it's against the law in most states, including California. Enforcement is pretty slack in the US (surprise surprise) but given that it involves employees making personal profit at the expense of employers companies generally would not tolerate this sort of behavior.

Do airline miles, hotel points, and car rental loyalty rewards count, and credit card rewards count?

Whoever is earning the rewards can earn quite a bit by choosing a higher priced options since it earns them more.

Was referring to company kickbacks (rebate) not personal profit

More likely someone in Finance or purchasing negotiated a preferential deal on behalf of the company.

Preferred supplier relationships are common in corporate America, for example "all employees fly United unless United doesn't go there," or "all employee car rentals are with Avis unless Avis doesn't serve that airport," or "all employee computers are HP unless there is a special exception," etc.

The company might get a partial rebate?

I have never heard of anything remotely like that from the HR side.

I have definitely heard of negotiated travel deals where the company gets some percentage of the spend back. So for instance a Delta flight might not be cheaper than United on the ticket booking site, but it ends up costing the company less. OTOH this was a Fortune 100 company with high travel spend so they had quite a bit of leverage.

There's a big difference between the company getting a deal vs. specific people in the company getting a kickback.

Are you the same person as GP? Because that's not the same username...

Perhaps you're speaking more generally, and saying that you've never heard of shady decisions made by HR dudes? Well, I have heard of such decisions, and I doubt I'm alone.

Shady decisions could be anything, this is specifically alleging bribery and corruption.