Here is the dbms_output contents by executing that pacakge in a different environment with same prod data.
Code:
SQL> set serveroutput on size 1000000;
SQL> exec pkg_get_exam.get_all_exams_by_user_id(2528666, 'C', 3, :c);
UserId= 2528666                                                                 
in_student_type= C                                                              
v_Assessment_Locator = 8D9A40AF-728A-86DC-9BE4-B7C68FF6AD66-1::AS               
v_Assessment_Locator = 8DA04C61-728A-86DC-9BE4-B7C6AC2CAE1B-1::AS               
v_Assessment_Locator = 8D9BA966-728A-86DC-9BE4-B7C68D109065-1::AS               
v_Assessment_Locator = 8DA2310F-728A-86DC-9BE4-B7C665C6D818-1::AS               
v_Assessment_Locator = 8D9E08AD-728A-86DC-9BE4-B7C6E64CA4D7-1::AS               
v_Assessment_Locator = 8DA2A9A0-728A-86DC-9BE4-B7C6F0776018-1::AS               
v_Assessment_Locator = 9878E785-728A-86DC-9BE4-B7C6BE952F9D-1::AS               
v_Assessment_Locator = 9879786A-728A-86DC-9BE4-B7C66FF45CE2-1::AS               

PL/SQL procedure successfully completed.

Elapsed: 00:00:00.00
As you can see, it is writing very minimal to the buffer and it does not call any other package and it is not inside a LOOP. How could this output have exceeded 1MB ? I am seeing this error in 1 enrionment, not in the other. They both are 9.2.0.7.

Thanks.