That isn't what Harry himself says happened. From his book:
Harry writes that he received a phone call from an unknown number on September 8, 2022.
“It was my father. The health of my grandmother had deteriorated,” he writes, adding that Charles was already in Balmoral.
“Straight away I wrote to Willy to ask if he and Kate were going to fly there and, if so, when and on what terms.
“He did not reply. Meg and I looked up flights. The press started calling. We could not keep on putting off the decision.”
He adds that he and his wife cancelled a scheduled appearance at a charity awards in anticipation of both rushing to Scotland but adds: “Then my father called again. He told me that I was welcome in Balmoral, but... without her. He started to explain his reasons, but they made no sense, and it was disrespectful.”
Harry says he told Charles: ‘Don’t even think of talking like that about my wife.’ before realising that there had been a misunderstanding.
“Apologetically, he stuttered that he simply didn’t want it to get crowded. No-one’s wife was going to go, not even Kate, he told me, so Meg shouldn’t either.
Harry adds that he told his father: “You should have said that at the start.”
Having boarded a chartered plane, he said he “spent almost the whole flight looking at the clouds, reliving the last time I had spoken with my grandmother (he goes on to describe the conversation in detail)........The Duke adds: “When the plane started to descend I saw that my phone lit up. It was a message from Meg: “Call me when you get this.”
“I looked at the BBC website. My grandmother had died. My father was king.
“I put on my black tie, got out of the plane under heavy rain and shot up to Balmoral in a borrowed car.”