Temperature Monitoring

I'm not familiar with ACHC.  I would recommend you consider these supplies as a working supply.  Keep that supply to a minimum, say only enough needed for the short term. For instance, if the supply is good for 12 months at 2-8C but if stored at room temp only good for 12 weeks, then be sure they only have enough of the working supply to last less than 12 weeks in case the fridge goes out or they leave at room temp.
Your policy should state that only a small working supply is maintained at the point of testing.  You could then state that the main supply stored in the lab/POCT is monitored for temp/humidity but the small working supply is not monitored.  I would think if the nursing unit has a fridge being used to store other supplies, it would be monitored by someone- maybe pharmacy??

I also am not familiar with ACHC.  I would expect that you would still have to monitor the temperature of the refrigerator regardless of the quantity or semantics used to describe them.
The question is: Are they being held to the manufacturers defined temp range for refrigerated storage to keep that expiration date or not?  Did the refrigerator fail?