The B767 actually has an APU which is certified to start at high altitude and cold soaked. It is checked regularly when maint puts a notice in the tech log to start the APU nn minutes prior to descent.
The fact that the B767 also has a RAT has nothing to do with not running the APU continuously on an ETOPS sector.
As for checking the cross feed valve every sector, we always expected that it would be worn out the one time we needed to use it in anger. Later deliveries came with two cross feed valves, hence no in flight check required.