Yes, of course it is our fault. /s
When someone says, for example, that the Germans invaded Poland in 1939, he is automatically insulting Ludwig van Beethoven, Marlene Dietrich, Martin Luther, Albert Einstein, etc, etc.
He is also insulting the Polish, and anyone born in 1939.
So the PC version of “the Germans invaded Poland in 1939” is “the * invaded the * in *.”
She needs to learn the difference between imply and infer. O’Reilly implied nothing about ‘all Muslims’ or those she named. She inferred that meaning!