Personal anecdote: I wanted to change the credit card on the order. So I went to the Nexus page[1], clicked "Customer support" in the sidebar, clicked "Managing your order", and called the number they show, 1-855-83-NEXUS. Someone picked up in maybe 30 seconds (and I expected really bad wait times for Google customer support...).
I explained I wanted to change the credit card, and he asked me for my email address + a piece of personal information. He told me he couldn't change the credit card, but could instead issue an order cancellation and I could rebuy the Nexus 7. Not ideal, but I said it was okay (after confirming that they weren't out of stock or anything). He saw that I only had one order on my account, cancelled it for me, and we ended the call. No order number needed; took all of 4 minutes.
Granted, I'm a pretty big fan of Google so I'm definitely biased. And I do agree that Google's customer support sucks. But it's a bit disheartening to see the top comment be such a petty complaint.
[1] https://play.google.com/store/devices/details?id=nexus_7_8gb...