The claim is in any case preposterous. To do open-heart surgery you have to open the chest. If you do that, the patient cannot breathe by the usual negative-pressure means, and will quickly die unless artificially ventilated with positive-pressure. In order to do this, the patient has to have an endotracheal tube in place, and it is impossible to place such a tube unless the patient is anaesthetised, by which I mean unconscious to the point where the cough reflex is suppressed.
This trick is similar to the one showing a lady being sawn in half. The only difference is that nobody seriously expects the audience of the latter show really to believe that a lady has indeed been sawn in half.
Even where lesser claims are made for acupuncture anaesthesia, such as orthopaedic surgery being performed, it's still a case of "please ignore the man behind the curtain", or in this case the I/V drip which is of course only delivering saline, it couldn't possibly have any morphine in it, could it? Many Chinese statistics on acupuncture "anaesthesia" openly admit that other regular painkillers have been used in conjunction.
And finally, European surgeons used to do quite complex stuff before anaesthetics were discovered. The father of the Bronte sisters had surgery for cataracts, apparently quite successfully. J. S. Bach also had eye surgery shortly before he died in 1750. The amount of pain patients can soak up in that situation varies considerably but is often a surprising amount.
But anyway, open-chest surgery without intubation is just flat impossible.
Rolfe.