I dont usually post here but since this is regarding Covid and may lead into disinformation I might as well jump in.
Los Angeles County Public Health is in charge of Covid testing in the County. Only Pasadena and Long Beach have their own Public Health Departments. The mayor of Los Angeles has no authority over the 36 testing centers in the County. The testing centers near my home we're active all throughout the day.
After reading news articles the information is completely mixed. You cannot find out which testing centers are actually closed and how long. This is what is frustrating about claiming "All LA Testing Centers are closed". Was the Dodger Stadium testing center closed? Were the testing centers near Fairfax and Downtown closed? Were all of the County testing centers within LA City closed??
I have not found anything claiming anything. If all testing centers in LA City were closed at 3 PM, that leaves what like 2 hours of time with no tests?
Even if all testing centers in the City of Los Angeles are closed, which would be a shame, you can drive 20 minutes in any direction in this County and end up in a testing center. Please dont let this deter you from going to get tested.
Edit: I watched the video again and Garcetti makes it seem like they were closed for safety reasons due to LACFD and LACSD Department involvement with the testing center. He goes into the protests afterwards which would make it seem like they are related but I do not see a direct link in stating that he is doing it to punish protestors.