Global Database properties such as OWNER etc. are always given with SCHEMA names in a pg_dump output.
However, for non-global database objects, as far as I know, there isn't any way to get SCHEMA names prepended to all the database objects. The way the script works is that it sets the SET search_path before-hand all Schema specific database objects... which is more efficient and has the same effect.
In case you are trying to parse an pg_dump output to extract a given SQL line that works independently, you may have to also parse the nearest-preceding SET search_path line and execute that before executing the target line (for e.g. ALTER TYPE) to have the desired effect.