You haven't explained why Google wouldn't know about PH/BP.
In Apple's implementation which I do know well the WiFi triangulation is enabled even at the coarsest resolution. Which is obvious since it is low cost. So if indeed there is one SSID/MAC in the area and it is coming from BP why would Google not know this ?
The presence of a SSID isn't indicative that you went to said business. If I lived above a McDonalds, Pizza Hut, and Subway, all with their respective SSIDs, that doesn't mean I am at any of the businesses. So sure, Google could know that there's a Pizza Hut near you, but they have no way of knowing whether you're actually at the Pizza Hut, or, say, the Tesco next door.
In Apple's implementation which I do know well the WiFi triangulation is enabled even at the coarsest resolution. Which is obvious since it is low cost. So if indeed there is one SSID/MAC in the area and it is coming from BP why would Google not know this ?