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.