After meeting with doctors' lobbies yesterday - the Australian Medical Association, and the Royal Australian College of General Practitioners - Hunt published an after-hours media release announcing the change.
However, in its own question and answer publication sent to doctors, the Australian Digital Health Agency, which runs the record, admits there have been nine data breaches associated with the record.
The Government will also work with medical leaders on additional communications to the public about the benefits and objective of the My Health Record, so they can make an informed choice, he said.
"Concerns have been voiced in the rural and remote health sector that My Health Record information could be accessed by agencies like the Tax Office and Centrelink without a court order", Mr Diamond said.
"No documents will be released without a court order", Hunt said in a statement. "This will be enshrined in legislation", Hunt said.
The government will redraft part of the My Health Record legislation to make it harder for agencies and police to gain access to the contents of an electronic health record.
Health Minister Greg Hunt has made the concessions in the face of growing public concern about the record.
Trent Yarwood, an infectious diseases specialist and member of tech advocacy group FutureWise, told The Register there's no detail beyond "there will be changes".
"Don't be fooled by the Minister's backdown on a couple of aspects of the #MyHealthRecord privacy concerns, there are bigger problems remaining".
We very much doubt this will entirely put the matter to rest, and My Health Record's flaws - particularly its forced opt-in approach belief that its data is unhackable - are likely going to be held to even more scrutiny, but this is a start.
The Australian Council of Social Services boss Cassandra Goldie welcomed the decision and urged the government to now rebuild confidence in My Health Record.
People who did not have access to a computer to opt out online could ring the My Health Record opt out hotline, he said.
"After the assurances we received last night and the commitment to strengthen the legislation, we can now move forward and have certainty around the protections to the privacy of those records that our patients expect".
He added that the legislation would also be amended to ensure that if any Australian wished to cancel their record, they could do so permanently, with their record deleted from the system.
Yarwood also highlighted that even with law enforcement access dealt with, there will still be almost a million health sector workers able to access MyHealth Record. The amendments will also allow individuals to delete their record after the opt-out window closes.