Plenty of sites use a different typeface in their favicon than the one they use in their logotype, e.g., Blogger, McDonald's, Nasdaq, and Bing.

All of those has used an existing part of their logo as their favicon.

That's true for McDonald's, but certainly not the other three.

All of them has a favicon which is also a part of their logo.

But all three logos were designed and introduced at the same time as their corresponding favicon. Your claim was that the favicon was just a copy of an existing part of the logo.

Your claim was that a favicon could be a different font than in the logo. But these examples are all a part of the logos. Google would have needed to rebrand their logo to do the same.

The claim was, "Using a different font [on your favicon than the one you use in your wordmark] would make absolutely no sense."

I believe I have successfully refuted that claim.

I think you're mistaking their symbol for "a different font". Each one of those has a logotype and a symbol, which make up their visual identity (the word 'logo' is used interchangeably for those, or their combination). They are merely using the existing symbol as favicon - the stylized N/B/B. Google's symbol at the time was the uppercase G in the same font, so creating a new one for the favicon would be considered a rebranding.