Description:
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The set_error_handler() documentation contains:

It is important to remember that the standard PHP error handler is completely bypassed. error_reporting() settings will have no effect and your error handler will be called regardless - however you are still able to read the current value of error_reporting and act appropriately.

This is inexact. The standard PHP error handler is only bypassed for errors of a type included by $error_types. Even then, the $error_handler description suggests that the standard PHP error handler is not even bypassed:

"If the function returns FALSE then the normal error handler continues."

The whole page is very confusing regarding what happens to the normal error handler.