You're right. You seem like you've got it figured out already. It would be interesting to get a confirmation from another owner of your motherboard. But, you'd think there would be complaints on it's feedback page.
Motherboards don't usually require the -5 volt pin anymore. I don't think any new motherboards require it for that matter. And if it did it should've been specified in the specifications page. That's very odd.
I would contact the manufacturer and see what they say about it requiring a -5 pin.
You should probably return it to Newegg.
If it does require a -5 volt pin the manufacturer should be slapped upside down, up and all around and I would have Newegg send you a shipping label for an exchange for another motherboard. I certainly wouldn't keep a mobo like that.