In reality it depends on how the school was approved. Most of the time yes it means they can do their own examinations for private, inst, commercial, etc... Generally the only ride they are not allowed to conduct exams for is the CFI initial. They can typically perform exams for the remaining flight instructor tickets. However, I have seen a few schools that are allowed to test for all of the flight instructor courses. Some schools, like OU, just have to send their students to the FSDO for one CFI ride so they will do the CFI initial in house and then send the students to take their CFII with the FSDO. Aagain though it just depends on how the school was certified.