No, that's not true.
Say for example I buy an OEM version of Windows, and install it on my PC. Then I get a new system, and install it on that. It wants me to call Microsoft to activate, so I phone and lie that I had to format because something failed. I get a new code, and Windows activates perfectly, and Genuine Advantage lets me download all the great freebies.
It looks fine, runs fine, but is in violation of the OEM license, and therefore isn't a licensed product. Now that might not bother anyone, but like I've said numerous times in the thread, why bother spending money on it if you have no plans to adhere to the license agreement anyway?