Why is LOG level below WARNING and ERROR for log_min_error_statement?

Hello,

I'm trying to debug a problem that is occurring rather rarely, which
causes multiple clients connected to the same postgresql 9.4 server to
crash at the same time.

These clients send *lots* of SQL statements. I want to turn on
statement logging, but I am baffled by the fact that the LOG level is
*below* WARNING and ERROR levels, for the `log_min_error_statement`
configuration option. This results in my log being flooded with
useless messages about statements that have succeeded.

Why is it designed like that?

How do real DBAs deal with that (I'm not a real DBA, just a Python/C#
developer)?

Best Regards,
Kal