What the parent is saying is that's precisely the difference. Your wife brought her phone to the manufacturer.
The Nexus phones were not manufactured by Google. If I don't buy it from the Google store, my buying didn't establish a commercial relationship with them. The Pixel phones, though, are manufactured by Google.
Disclaimer: Even though I'm a Google employee I have no idea how these things work. I'm just clarifying what the parent said, which sounds likely to me.