This is true and even IF the inspector is called in and orders repairs ,the LL can always ask for an extension ( to fit a contractor's schedule ).Keep in mind that if LL hires someone to do the repair, it may take longer and you will still have to pay rent while the repairs are being done and waiting for contractor to start repairs.
Keep in mind, that a contractor time frame is when HE can fit the work in, not you nor the LL.
Also , I lived in a 4 unit Apt. house in upstate NY. It also had drop ceilings .
The LR ceiling Begin to droop ( their was also water leak from the roof ).
The LL had a contractor redo the LR only .
There was also paint/plaster dropping down on the ceiling in other areas and it posed no harm .
The LL can always have heavier tiles installed to hold the weight .
As a matter of fact , if one tile is missing or damaged the LL can simply replace it if the rest is otherwise stable .