This is literally what Canon does with printers btw. HP literally buys printer mechanisms from Canon, and then they sell it as their own printer, and they've done this since the early days.
HVAC equipment is the same way, other than Lennox and maybe Trane most of it is off the shelf with similar or identical parts and different logos.
When I worked at a car repair shop I was also told which brands were the best to buy for parts. Namely; when buying European cars you'd always buy Bosch parts because they were always what the VW/BMW/Benz dealer sells at a markup, and there was a similar brand for Japanese car parts. I've seen Mann filters and Hella horns used by all 3 as well (currently own a VW). I know of a few Japanese OEM suppliers but the names don't come to mind right now. Sure you can't use VW parts on a BMW but the same company will make both parts.