He may have violated a Google workplace rule.

But if they would have let him stay, and posted reprints of his ignorant, foolish memo at every doorway and every water cooler in the building, he may have resigned in shame. And Google employees would have come together in solidarity, agreeing that the guy is so small.

Instead you've divided employees, not over what he said, but that he's not allowed to say it.  

And then, instead having the cojones to beat him in court when he sues you, you'll "settle out of court," proving again that all you have to be is an idiot with a big mouth to get a sweet settlement.

Great achievement, Google.  Carry on.