Yes, it is correct. When it says "any 4 tax years" it means for a total of 4 years across any amount of tax years. So, once you use it 4 times, then that answer will change to YES and you will be limited to using either the Lifetime Learning Credit or the the Tuition and Fees Deduction.
Here are the full instructions for that Line
Line 23
If the American opportunity credit has been claimed for this
student for any 4 tax years before 2016 (including any year for
which the Hope scholarship credit was claimed for the student),
the American opportunity credit cannot be claimed for this
student for 2016. Check “Yes” and go to line 31.
If the American opportunity and Hope scholarship credits
have been claimed for this student for 3 or fewer prior tax years,
check “No.” See Student qualifications, earlier
