Primary Key and Indexes, are they necessary?

We have an Oracle aplication (developed by a vendor) which has about 150 tables.
However there is no primary keys on any tables. There are only about 30 non-unique
indexes (some of them are added after we requested).

The vendor responsed that the reasons they do not add the primary key and nessary
indexes are:
1. The index will slow down the data entry 2. While adding primary keys can enhance performance in Oracle DB, it can also degrade
  performance. For example, if a code table contains fewer than 30 rows (not sure the exact
  cut off), it is just as fast if not faster to do a full table scan for the information you are looking
  up. Especially, if the DB is not fragmented. Doing an indexed or Primary key look-up in a
 table of that size would cause jumping of the disk read/write head, while a sequence read
 can complete much faster.
3. They have several individuals with over 20 years of experience working with Oracle
  (meaning they have more experiences on Oracle databases).

Questions: Are these valid arguments? Should the primary key and necessary indexes

                 be added or not?

Thank you in advance.

John Chen
jochen_at_nygh.on.ca