Okay, I think I tripped on the semantics. If you're talking about software that sends usage information back to the manufacturer, that's usually in a user-mode application that gets installed with the driver. I've never heard of the device driver by itself calling home, nor of it being possible, since all the driver is supposed to be able to do is bridge the OS to a piece of hardware at a low level, and creating a TCP/IP connection to the Internet happens at a much higher level. You could have a kernel-mode driver installed as part of a rootkit, but that's a different thing entirely. It's nearly always possible to remove or defeat those bundled user-mode applications and still use the driver.
I expect that your contractors were tasked with doing just that -- divorcing the bloatware from the drivers and repackaging them without it -- since actually rewriting the drivers would require intimate knowledge of the specific hardware device, its firmware, its communication protocol, and all its nuances, and manufacturers don't typically release things like that. That's interesting, though. I'm glad to see someone taking this seriously as a security issue, because we don't know what's really included in the "anonymous usage statistics".
FWIW, the first thing I do when I buy any Windows device is to make a backup of the OEM preload, reformat the internal disk, and reinstall everything minus the bloatware from a known good source, as you also described. That kind of project can take days to figure out, and I'm sure I'm not as thorough as your contractors were.