drush_backend_batch_process not running non-core functions without $batch['file']

I've updated the documentation for Processing batch jobs with drush to reflect this problem and provide a way around it.

In my case, core functions like node_save() were executed but not the functions in my .module file;

this worked: $batch['operations'][] = array('node_save', $a_args);

this didn't work: $batch['operations'][] = array('my_module_function', $a_args);

However, once I set $batch['file'] to the path of the .module file

$batch['file'] = drupal_get_path('module', 'mydrushmodule') . '/mydrushmodule.module';

the functions were executed.

I assume that if a function is within a .module file and the module has been installed and activated, the regular core batch_process() can find and execute any functions in that .module file and that drush_backend_batch_process() should also find and execute them.