I don't think that is absolutely correct. I recently had troubles with my (Dell) motherboard. I received a new one from Dell (under guarantee) After installing it, I booted up and found that activation had been completed automatically, with reference to my digital licence
But, it looks like a hit and miss affair. As my situation was a repair, I guess this statement covered it:
"Changing the motherboard, however, generates a new installation ID. Under Microsoft's licensing rules, your license is valid if you replace a motherboard because of hardware failure. You need a new license if you chose to upgrade the motherboard, because you're essentially building a new PC."
But, I read that this site (official) is still quietly working for most:
Link Removed