Not to users. The user who types Wal-Mart into their address bar expects to communicate with Wal-Mart. They aren't going to check if the certificate matches. Only that the icon is green.

This is where the disconnect comes in. Me and you know that the green icon doesn't prove identity. It proves certificate validity. But that's not what this is "sold as" by the browser or the security community as a whole. I can buy the domain Wаl-Mart right now and put a certificate on it that says Wаl-Mаrt and create the conditions for that little green icon to appear. Notice that I used U+0430 instead of the letter "a" that you're used to.

And guess what... The identity would match and pass every single test you throw at it. I would get a little green icon in the browser and my certificate would be good. This attack fools even the brightest security professionals.

So you see, Identity isn't the value that people expect from a certificate. It's the encryption.

Users will allow a fake cert with a green checkmark all day. But a valid certificate with a yellow warning is going to make people stop and think.