While there is much angst in some circles around the idea of a national patient identifier, given privacy implications, the reality is that we need one if we want to have reliable, mobile medical records. It is the only way to ensure that a patient's medical records at any hospital or provider refer to that patient and that patient only.
Absent that, we're forced to rely on some sort of algorithm to match records from multiple systems. For instance, in my work with BMC2, we need to match records of patients in an internal system with those in the National Cardiovascular Data Registry, published by the American College of Cardiology. We use a handful of fields that get us to a roughly 98% match rate, which is very good. But, we're in a very controlled environment, only have two data sources and both sources are maintained by study coordinators whose full-time job is managing registry data. We should have a match rate that high.
Of course, a single identifier isn't foolproof, especially if it is entered by hand or otherwise managed in some manual process. Plenty of data is fat-fingered, transposed, even entered by mistake (Patient A's Id entered in Patient B's record), simply because a human being is part of the process. That will likely never truly go away, and we'll always have records that aren't in a pristine state due to problems with the identifier. But, those can be fixed, as needed, by adding or editing the correct identifier.
However, that's an entirely different issue than an identifier that doesn't exist.