They're not doing business with another company in any meaningful sense. There's multiple companies set up with the same owners so they can pretend the one in the lower tax region makes all of the revenue, often through IP licenses that look like expenses to the entity in the higher tax region. It's financial engineering that doesn't reflect where value is actually being created or revenue captured.

I'm not a CPA, but my understanding is as a US citizen, your closest analog would be setting up an irrevocable trust. But, then you no longer have control of those assets. Owners of these shell corporations are able to effectively control their assets. Naturally, if they were legitimately doing business with a 3rd party company, they'd have no say over what that other company can do with their revenue. That's a key difference between what's a normal business operation and what's a shell game for tax avoidance.