If they feel like their is mold although someone has already inspected for that ... you can get one of those water scanner things (sorry I have no clue what it is called) but it essentially checks for moisture (it shows certain color based on the moisture) also I would remove the base boards and cut about a foot of the dry wall to see if that is wet.

Address the water/moisture problem first, then remediation.  

Add in water/moisture sensors, etc and you could have a fully-wired house sending you alarms to allow early intervention to what could become major issues.

(from our core rental agreement)Mold may grow and exist in any structure where there is, or ever has been, a presence of moisture and a food source for mold to grow.Its presence may exist without the knowledge of the structure owner and may be concealed from the untrained observer.Some varieties of mold are toxic and may cause adverse reactions in certain individuals.Tenant and Landlord will complete a Mold and Moisture Hazards addendum that will become part of this rental agreement.MOISTURE AND MOLD.

I’d rather trust a professional with a moisture meter to see if it’s dry (just after or even during a heavy rain would make me feel better) before fixing the ceiling.

The first part of Mold remediating is stopping the moisture issue  until you figure out that part don't bother with step 2 . 

He’s put in tile and LVP floors so no carpet to clean or replace, the bathroom lights are wired with automatic fan turn-on which prevents moisture accumulation resulting in mold, etc.  

Tenant agrees to allow Landlord timely access to premises to do maintenance and repair.Tenant will notify Landlord in a timely manner of any damages or problems as they arise, including damages caused by Tenant, malfunction of appliances or fixtures, and water/moisture leaks and spots.Tenant will care for the premises, keeping them clean and clear of debris.""

Completely shutting off utilities for a prolonged period of time can damage the property since it will not be climate controlled for that period which can lead to moisture damage, mold, and other costly repairs if it goes on long enough.

Because if it's not, you are going to be spending a lot of that $200 a month painting and dealing with moisture issues.