You both got it wrong. Limited User has Write access, but only for a certain subset of tables. For tables not included in that subset, the following applies: during one NAV/BC session, Limited User can insert/modify only 3 of those non-included tables. If he/she would try the same on the 4th table, the error would get thrown.
For example, tables Payment Terms, Currency, Country/Region and Item are one of those not included tables. Limited User could modify the first 3, but when trying to modify some Item record (during the same NAV/BC session), it would fail.
Also, bear in mind that table G/L Entry is explicitly prohibited to Limited Users, which in combination with this limit of 3 tables makes them unable to post anything.
All of this CAN NOT be changed by setting any kind of permissions/permission sets, otherwise it loses its purpose.