Sounds like you have a common PLAN_TABLE in your database and this user can SELECT from it but not INSERT.

For example, I have a plan_table created and a public synonym on it. I then created a user a and did the following:

tkyte@TKYTE816> grant connect, resource to a identified by a;
Grant succeeded.

tkyte@TKYTE816> grant plustrace to a;
Grant succeeded.

tkyte@TKYTE816> grant select on plan_table to public;
Grant succeeded.

tkyte@TKYTE816> connect a/a
Connected.

tkyte@TKYTE816> set autotrace on
tkyte@TKYTE816> select count(*) from dual;

COUNT(*)
----------
1

ERROR:
ORA-01031: insufficient privileges


SP2-0612: Error generating AUTOTRACE EXPLAIN report

Statistics
----------------------------------------------------------
0 recursive calls
4 db block gets
1 consistent gets
0 physical reads
0 redo size
367 bytes sent via SQL*Net to client
424 bytes received via SQL*Net from client
2 SQL*Net roundtrips to/from client
0 sorts (memory)
0 sorts (disk)
1 rows processed

tkyte@TKYTE816> connect tkyte/tkyte
Connected.

tkyte@TKYTE816> grant all on plan_table to a;
Grant succeeded.

tkyte@TKYTE816> connect a/a
Connected.
tkyte@TKYTE816> select count(*) from dual;

COUNT(*)
----------
1

tkyte@TKYTE816> set autotrace on
tkyte@TKYTE816> select count(*) from dual;

COUNT(*)
----------
1


Execution Plan
----------------------------------------------------------
0 SELECT STATEMENT Optimizer=CHOOSE
1 0 SORT (AGGREGATE)
2 1 TABLE ACCESS (FULL) OF 'DUAL'




Statistics
----------------------------------------------------------
0 recursive calls
4 db block gets
1 consistent gets
0 physical reads
0 redo size
367 bytes sent via SQL*Net to client
424 bytes received via SQL*Net from client
2 SQL*Net roundtrips to/from client
0 sorts (memory)
0 sorts (disk)
1 rows processed

tkyte@TKYTE816>