The thing is that you actually can't prove that Apple didn't put those parts in there, if they're sourced from the same suppliers Apple sourced them from. They're literally "the same" parts, so no regular inspection would find them.
That's what I meant by "the computer thinks it's a Mac": Apple already has code in place to detect when you've used parts that don't belong in Macs, in your Mac. (That's DSMOS — "Don't Steal Mac OS X", a kernel extension that verifies the hardware on boot.) But if Apple used some random IC from Samsung or Broadcom, and then the repair shop replaced it with the same random IC from Samsung or Broadcom, but not sourced through Apple, then Apple can't tell—at least through any traditional means—that that computer has been tampered with.
And it's important to tell, because Apple does QA (burn-in testing, etc.) on the parts they install. So a random Samsung or Broadcom chip might be a lot more flaky than the same Samsung or Broadcom chip that has survived through Apple's testing gauntlet. And if Apple can't tell that the chip has been replaced, then they can't void your warranty—which means the flakiness of the replaced part becomes negative media coverage about Apple, rather than just being a story about third-party repair shops using non-QAed parts.
(Remember when Apple used those GPUs in old 2011-era MBPs that would overheat enough to de-solder themselves? Imagine if that wasn't Apple's fault, but rather the fault of repair shops replacing Apple's shipped discrete GPU with "the same" discrete GPU that hadn't been through Apple's QA.)
The verification software can detect this specific problem, by comparing lot numbers for each part in the system to lot numbers Apple's factories have actually received. Thus, even a lot of parts that Samsung created exclusively for Apple, but never shipped to Apple, and instead sold to some reseller, would show up as "invalid" here. As it should—because Apple hasn't picked out the bad parts from the lot.
Now that I think of it, a potentially-useful analogy is the 2007 mortgage crisis. People were buying CDOs (income from mixtures of mortgages, that pay out when people pay their mortgages) endorsed by respected institutions, who gave them high ratings. But the mortgages that went into these CDOs weren't actually verified in the way that the institutions promised, and so they failed a lot more often than they should have for the quality ratings they were given.
In this analogy, Apple products are like highly-rated CDOs; and the verification software being discussed here is what's required to actually check that the parts in the computer (i.e. the mortgages in the CDO) belong with that quality-rating slapped on them.