The data center where I work has large diesel generators for power cuts. They are electric (battery) start. There is no capability to start them manually. The batteries are on maintenance chargers that keep them in good condition. The generators are started and tested every two weeks.

Could the batteries be dead and the generators not start? I guess but it's very unlikely. I get that on an oil rig it might be a matter of life and death and you need some kind of manual way to bootstrap but there's not much that's more reliable than a 12V lead-acid battery and a diesel engine in good condition.

It's unrealistic, and if one power station is unable to use their batteries to start their emergency generator (through the absurd incompetence you describe, or more likely through a major fire, flood or assault) the grid can be started from a different one.