I am not sure this is accurate.
They made an initial statement about the abdominal surgery.
Then radio silence while the rumours swirled because there was no sign of her whatsoever. And while the rumours themselves were wrong it was true that the palace were holding back something (the cancer diagnosis)
Then they faked a photo which made it a lot worse
Then she did the stripey top video message and by that point she kind of had to do a video message because the photo fake had made all the rumours so much worse.
Actually if they had issued a statement about the cancer treatment before the rumours had started and not faked a photo, a written statement might have been enough. We won't ever know.
I think they have messed up the PR throughout