For NT 5.x era volume licensing and 5.x/6.x retail licensing, this is pretty accurate. However, until Windows 8, OEMs activated by what Microsoft called System Locked Preinstallation. OEMs put a marker/certificate into BIOS memory, which indicated what Windows version(s) the machine was licensed for. They then activated it with an SLP key, which just tells Windows to look in BIOS for license information, and find the license data. Windows will activate permanently if BIOS license data and Windows versions matches. Each OEM has one or a couple of SLP keys per Windows version, so millions of machines will use the same key. The license sticker on any machine has a unique key (COA key), but this isn't used when the OEM installs Windows, it's just there because doing an SLP activation isn't end-user friendly.
What pirates did was manipulate memory to put a license certificate in BIOS when one wasn't originally there, and activate with an SLP key. This was done either by modifying a BIOS update, or with a bootloader program that would put the certificate in memory before loading Windows. End result is that Windows thinks it's SLP activated by an OEM. There is no automatic way for Microsoft to detect this.
The only way is to find mismatches, for example an Asus X99-A motherboard is not sold with an OEM certificate in BIOS. If Asus sold it to an OEM who would need that in BIOS, they would rename the board, even if it physically was identical. If you put an OEM certificate in this boards BIOS, there is a mismatch, because a X99-A board isn't supposed to have that. Finding all these mismatches in a way that reliably identifies pirates and avoids identifying paying customers is a lot of manual work, and require a lot of research and testing.
With Windows 8 OEMs have to put a unique key in each machine BIOS, not just the generic license certificate. This makes OEM activation less useful, so pirates use fake key servers instead. Large businesses can set up key servers in their own premises, so they can manage licensing centrally. Pirates use programs that emulate keyservers, Windows can't tell the difference. Microsoft could implement extra checks if they found bugs in these emulated keyservers that would identify an unauthorized keyserver.