I think nowadays their would be quite a few who would take blood if they can be assured nobody else could know about it .And taking advantage of the strict visitor policy they could get away with this .
Of course the RN who is a JW could break confidentiality and spill the beans on anyone they know who is a JW to the Elders in the area where the patient lives ,and they could do this anonymously of course.
And a patient would not know or be aware of a RN being an active JW now would they.