>empowered to do pretty much anything required to keep the service up and running,

Is that really uncommon? I've been on call for many companies and many types of institutions and never been told once I couldn't do something to bring a system up that I can recall at least. Its kinda the job?

On call seriousness should be directly proportional to pay. Google pays. If smallcorp want to pay me COL I'll be looking at that 2AM ticket at 9AM when I get to work.