A mistake in "Op Amps for Everyone" about op amp attenuators
TL;DR
It's a mistake in the book.
Details
After some googling (and pirating for different editions of &quot;Op Amps for Everyone&quot;) I found that the original editor of &quot;Op Amps for Everyone&quot; (1-2 editions) was Ron Mancini. These editions doesn't contain the caution about \$R_G &gt; R_F\$.
At 3rd editions the editor of the book was changed to Bruce Carter, and &quot;Texas Instruments&quot; label from the title is gone. He placed that caution in many places around the book. He didn't remove the old material though, like the quote above about inverting and non-inverting circuits has the same loop gain (so the stability), which directly contradicts with the Carter's caution.
There are some other discussions on web, e.g. this with Ron Mancini itself, and this where Michael Steffes (from Texas Instruments) wrote:

This actually was a classic mistake by Bruce Carter that Mancini seems to paper over for some reason. Somewhere Bruce got the idea that an inverting configuration had a noise gain of Rf/Rg instead of the correct 1+Rf/Rg. Bruce Trump and I wasted about an hour one day trying to explain that error to him with no luck.