As annoying as this must be for them, it could be worse. I worked on an electronic health records system for a couple years, and the state required EHRs to synchronize pediatric vaccination records with their vaccination database, using name dob county of birth as the patient identification. We ran into a case where the vaccination records got merged for two patients with the same name and birthdate/place. The only reason it was caught was because one of the mothers had kept careful track of the medical records herself, and noticed the discrepancy while talking to the doctor. If she hadn't the doctor would have assumed the baby had already had the vaccination.
I hate to think how common this kind of thing might be, without anyone even knowing. It's one thing to have the sorts of problems described in the article. It's a whole new level of terrible when you consider that doctors are making medical decisions impacting your health and life based on records that could be mixed with somebody else's, and you would never know, since patients don't ever look at their own chart.