I've always reconciled the Fairview invoices against TASCS or Oncore. The study personnel rarely, if ever, see copies of the invoices - but they are the ones putting the subjects and dates into TASCS/Oncore, so I would consider that to be their "review."
I have had the "no name, no ID" issue come up before. Sometimes it's a generic study charge, and not related to any particular patient. Sometimes it IS something that seems to be related to a particular patient (as appears to be the case in this example). I have had success emailing JJ and asking for more info - if I recall correctly, sometimes I've gotten the additional info and sometimes the charges have just been removed. But I think emailing JJ/Fairview and requesting the missing info is the best first course of action.