Interestingly, The Guardian published their take on the speech at "18.17 BST", before the speech and the Q&A session were over, so it omitted Miliband's and Burnham's critical promise. The New Statesman's article admits to having been drafted over the previous weekend, but was not published until the actual day at 18.15.
"Andy Burnham has pledged to repeal the Health and Social Care Act if he becomes health secretary. This would undo the hospital closure clause, the wholesale privatisation, and reinstate the duty of the secretary of state to provide universal healthcare to the people who voted for them."
I cannot track down any coverage by the neo-liberal MSM of this stance against the privatisation of the NHS. I do not think it is because Labour has back-tracked. I suspect the dearth of reporting on this aspect is due this policy being popular and in-line with the electorate, which is far to the left of all main political parties, excepting the Greens.
I believe both Miliband and Burnham are honest men, honourable politicians; they will keep to their word I suspect.