I've been on 6 cruises... and always, always we get there, WAY before they say you can 'board'... like around 11am....
In my experience... even though they say '1pm' it's normally about noon a little after, when they start letting people on, unless something happens...
on our last cruise, they wouldn't let anyone off (I think they were searching the ship for something) we got off around 11am, kinda late considering....
so, I seriously doubt the next crew got on at noon that time... (we joked that if they didn't let us off soon, they'd have to feed us lunch...)