I'm thinking the Palace have told a fib about the due date and possibly location of the birth so Kate can get through it all in peace. It's what I would do and it would be hilarious to have all those paps outside the hospital for days for nothing.
I don't know about the Palace, but I bet this is what William would do if he could! There's little love lost between him and the more intrusive photographers, and if he was allowed to get one over on them he'd do it in a heartbeat!
First babies are often late - out of myself amd all my friends who've had babies over the years, 80% of our first babies were nearly 2 weeks overdue, and 50% of us were induced. Dates are rarely exact for expectant mums - too many variables! - and even then the only 'official'date the Palace gave was mid-July - specific dates were only press speculation or attributed to un-named 'sources'!
Whether you like Kate or not (personally I have nothing against her) all the status in the world won't protect her from feeling as anxious as any other first-time mum, and certainly won't help make an induction any better if she ends up with one (being induced isn't pleasant!) so I hope it goes well for her, as I would wish for any first-time mum.
Whenever it is!