Functions and triggers allow users to insert code into the backend server that other users may execute without knowing it. Hence, both mechanisms permit users to Trojan horse others with relative impunity. The only real protection is tight control over who can define functions (e.g., write to relations with SQL fields) and triggers. Audit trails and alerters on the system catalogs pg_class, pg_shadow and pg_group are also possible.
Functions written in any language except SQL run inside the backend server process with the operating systems permissions of the database server daemon process. It is possible to change the server's internal data structures from inside of trusted functions. Hence, among many other things, such functions can circumvent any system access controls. This is an inherent problem with user-defined C functions.
If you see anything in the documentation that is not correct, does not match your experience with the particular feature or requires further clarification, please use this form to report a documentation issue.