It's the polite version of the tantrum. Demands for more info have not and will not be met.
There is no dilemma, and I think it's a sign that they're in the "tell us more" camp that they want to present it that way.
Comparison to the King is misplaced - unlike PoWess, he continues to work (and send messages) but has cancelled/postponed all engagements where he would meet people (v sensible, given what cancer treatments can do to the immune system).
But at least they acknowledge that it's just public curiosity (and that does not outweigh her medical privacy)
The proper public interest - is her health going to impact on her role - has been answered ie she's had surgery, won't be working during convalescence, is expected to be back at Easter.