I don't think Harry approved or even knew what Rayner was going to say, fwiw.
I reckon Boshoff contacted Rayner and asked if he had anything to say about the debacle; Rayner contacted Harry and asked if it was OK if he spoke to the Mail on Harry's behalf. Harry, doubtless keen to have some positive media to counteract the criticism he's been getting, would have replied with a resounding Yes and also probably relayed his (or M's?) view that this all stemmed from SC's jealousy of the wonderful Meg.
Given that Harry has previously claimed on record that William, Kate, Charles and Camilla are ALL feverishly jealous of Meghan, this erroneous belief does sound as though it would have originated with H&M.
But I doubt Harry thought for a moment that imbecile Rayner would get on the phone and say all of that on the record, and with such a strong overtone of misogyny and racism.
If he DID, then he's stupider than I thought. And I already thought he was pretty fucking stupid.