There's a big push right now to implement such systems. Hospitals now have a monetary incentive, due to the ACA, to not have patients return for anything more than a follow up for something like 30 days after an emergency room visit [1]. I'm not sure what Apple has to offer in regards to this kind of data storage, but it's going to have to be HIPAA compliant if they want any sort of acceptance.
Also, a lot of what is being done is automated monitoring. An algorithm can be developed to measure, for example, blood pressure, and if the patient deviates from acceptable ranges, the algorithm can trigger a contact to the patient, their healthcare provider, and family to begin an intervention to correct the bad blood pressure.
Adherance (doing it when you're supposed to) and validity (the measurements reported for Bob Smith are actually from Bob Smith) are big concerns, and there are also a lot of things done to ensure that the patient is doing their part correctly.
[1]: http://www.acep.org/Legislation-and-Advocacy/Practice-Manage...