What I'm envisioning here is that someone goes for a biopsy and all of a sudden their insurance goes up and banks start trying to claw back all their long-term stuff before the patient dies; possibly before the patient has got the results back themselves. That's just two of the most obvious things that can happen; and is not what you really want if you've been diagnosed with something horrible.
From the sound of it, this information would be shared on a fairly broad basis and it's a statistical certainty that there will be an ethically-bankrupt money-grubbing bastard or two amongst the sharees; if not now then next week. Look at the shit Uber get up to with their data and they are just a taxi company. Extrapolate that attitude to serious stuff like life-threatening illnesses and think of who has a financial finger in the pie (insurance, banks, people the patient does business with; people who stand to inherit, medical profession etc etc) and things could get nasty very quickly.
For the path:
Patient --> GP --> Testing centre --> GP --> Patient
...you do need a unique identifier, name and history.
For the collaborative, analytic and statistical work you'll need a unique identifier (because that's how databases work); and I should imagine that some clinical details would be helpful too. The unique identifier doesn't have to have anything to do with the patient though in this context. You'd also have to be very careful with the clinical data too...it's *amazing* what people can fish out of databases. Off the top of my head a 2-system design; one with the patient's actual details that is rabidly secure, that also has an extra field for random numbers that you use as the unique identifier for wider dissemination. That way the patient could be identified/contacted; but you'd need a bloody good reason to gain access to the 'real names' system.
Not sure what you'd do for the clinical details...I'm not a Biomedical anything so am unsure what 'clinical data' is made of, exactly; so can't really offer suggestions on improving the safety/anonymity.
The business -as described in the article- is basically 2 distinct fields of operation with diametrically opposed data needs. Field 1 (diagnosing individuals and reporting results back) does need personal information. Field 2 (collaborating and letting Big Data munch on the numbers) needs to be as anonymised as humanly possible while still including *necessary* information.