My point, and you give George Martin's reference to it in Anthology, is that they had ALREADY recorded How Do You Do It. There is no evidence at all that he wanted them to record a second version of.
I agree that GM had some reservations about Please Please Me based on the original arrangement, but that he had something in the can if he felt the new arrangement wasn't good enough. He had nothing to lose by seeing what they had done since he'd told them to go away and work on it. Re-read your question though, "George Martin was initially reluctant to let ...