It has always been my understanding that after you invite the cops into your domicile the whole of it is open to them. That you have to demand a warrant at the entry door.
Yes, was my impression at one time as well. However, letting them in does not grant permission to search - consider, your neighbor calls the police because your stereo is too loud, they show up and you let them. This alone is not permission to search the home, to poke around your home absent PC.
Cheers.