It's not hard to become a phone maker these days, judging by the sheer number of Android OEMs that are out there (hundreds, I believe). If there was huge untapped demand for Android sans Google then a new company would appear, they'd download the Android code, they'd go to Shenzen and do a deal with a white label manufacturer, and they'd make such phones. Google wouldn't stop them because they'd be a company that doesn't make any other kinds of phones.
We know this is possible because there's one huge market where that's normal, China. Google's services are blocked in China anyway, so there's no point adding their app store or mapping apps. Local firms produce local versions of Android for their own market and it works fine. We also know this because Amazon tried it and they weren't sued or anything.
There are also open source spins of Android that have custom app stores like F-Droid. A new phone maker could ship those too.
In general, when you see an example that explains a complex issue you should assume that it is significantly simplified and therefore will not be realistic.
It's very normal that a company B would want to go to company A, if A already have a lot of expertise in Android. For instance a POS manufacturer might want to collaborate with Sony or Samsung on an embedded device which uses Android internally (without the GApps & stuff), but Sony and Samsung are forbidden from dealing with B.
Even Amazon would be happy to outsource some Android development to e.g. Samsung but they can't.
However, Sailfish is available only as a post market firmware.
Being a derivative work of AOSP courtesy of libhybris, it would seem Sony are prevented from factory installing Sailfish on any future Xperia device.