If your exam is re-scored and your new score is lower, can you keep your higher score?

I’m considering having an exam re-scored. I got a four; believe me I’m happy with it, but I made an error on the scantron and know that there could have been an issue with the machine scoring the exam. If I were to have my exam re-scored, and I got a lower score, could I keep my four or would I get the three or lower. The only reason I’m considering this is because the universities I’m applying to require multiple fives on AP exams for admission of US students. Please post if you have prior experience with a similar scenario. Thanks.

Straight from the College Board multiple choice rescore form:

"For a fee of $30 per exam, you may request to have your multiple-choice answer sheet rescored by hand. After your answer sheet is rescored, that score and your free-response score are then weighted and combined and converted to an AP® score. In the event that the score is different from the one that was previously reported, the newer score will prevail, and your college will be notified of the correct score by mail. Up to eight weeks after your request is received, you will receive a letter confirming the results of rescoring. Because AP scores of 1–5 represent the composite score of the two exam sections, raw scores for the individual multiple-choice or free-response sections are not available. The free-response section is not rescored.
Important Notifications
•** Multiple-choice rescores may result in higher or lower scores than first reported. Results are FINAL and will automatically be rereported to all designated score recipients. **
• You cannot appeal or reorder a multiple-choice rescore. "