It doesn't appear to be an addon (it's a controller called documents). The print_invoice menu item uses orders.print_invoice mode which only passes the 'type' (pdf, etc.) to the fn_print_order_invoices() function as the parameters. Hence since the param['template_code'] is not passed, it defaults to 'invoice' and that is what's used fro renderById().
It seems there's a whole layer of configuration settings that is missing from this functionality. There does not seem to be any way to assign various 'types' of documents to different functionalities.
I guess the only way to address this is to use a pre controller and pass the 'template_code' parameter and then redirect so the standard controller/mode is not used.