No, it does not. But, the fact that your chlorine has dipped so low may be causing a chlorine demand if you have an impending algae bloom.

On the other hand, could it be testing error?

Watch these testing demos to verify that you are doing it correctly.
http://pool9.net/K2006-vid/

If you are certain that you are, then I would advise going ahead and shocking the pool. Add 3 of the 121-oz jugs of generic 8.25% bleach. An hour or two later, test again and make note of the FC and CC readings. Then, in the morning within an hour of sunrise, test FC and CC again. Post your evening and morning readings for us to see.