I don't think the absence of an elevated White Blood Count in itself rules out an inflamed appendix. It could be in indication that it's not on the point of perforating, and that an operation to remove it might not be needed.

A good few years ago my wife got this pain on her right side. "Not your appendix", said the GP - "constipation." Less than 24 hours and she was on the operating table having her appendix removed...

As PA said, sometimes you have to be pretty firm with doctors. I hope there'll be good news soon, and she'll be back home being fussed over.