The difficulty here is that in the example above, it's unlikely, given any amount of scale, that the two people were on the same team. They were doing different things with the same data and probably didn't know what the other was doing.
Sure you could add a convention to your 'how to log' doc that specifies that all user input should be tagged with double '#' but who reads docs until things break? convention is a shitty way to make things work.
There's 100 ways that you could make this work correctly. Only restarting on a much more specific string, i.e. including the app name in the log line etc . . . but that's all just reducing the likely hood that you get burned.
I've also written a OOM-Killer.sh myself, I'm not above that, but it's one of those edge cases that's impossible to do correctly, which is why parsing and acting on log data generally considered and anti-pattern.