First of all we must remember that just because someone is 'in command' it doesn't necessarily mean that they make the right decisions! When the wrong decisions are made it is up to all of us to learn by the occurance to help us in the future to make the right one.
Ultimately, the person in command is that person where the 'Buck Stops'. Just because you 'hadn't yet signed the tech log' would be a a poor excuse if something happened. At the subsequent enquiry for the most part the On-Comming Captain should assume command as soon as possible and certainly as soon as the off-going Captain leaves the Aircraft. If there is no on-comming Captain, then the aircraft should be left accordingly or 'handed over' to the engineers or whatever.
"So tell me Captain", says the man from the ministry, "When the APU caught fire, you did nothing because at the time you weren't in Command even though you were the highest ranking officer on the scene at the time?"
I hope you're well insured!!!