pg_dump and search_path

I have a custom search_path:

# show search_path;
           search_path
----------------------------------
 "staging, transient, pg_catalog"
(1 row)

I ran `pg_dump --schema-only` and the only reference in the output to search_path is:

  SELECT pg_catalog.set_config('search_path', '', false);

Then one of my functions which does not reference the full name of a table with its schema fails with "relation [rel-name] does not exist".

Is that a bug?  I have seen some old posts about this issue but am not sure if there is a ticket or why it still is an issue.

Thanks,