Actually, most reviews I've seen specifically mention Asus. Seems like they're in a winning situation: they're just about the only people making a profit on the Nexus 7.

Does their logo appear anywhere on the device?

It does appear prominently at the back [1]

[1] http://images.anandtech.com/doci/6054/GoogleIO2012-2261.jpg via http://www.anandtech.com/show/6054/google-nexus-7-mini-revie...

If you look closely at the bottom of this photo, yes. http://www.google.com/nexus/a-images/tablet-n7-features-usho...