This clears up a few things:
1.) The PlayStation 4 can play games offline without having to be online. This was clarified the day of the PS4's reveal back on February 20th.
2.) Sony will not have any mandatory DRM for used games. You can buy, play, trade used games on the PlayStation 4 just as usual. No additional registration fees, pay-walls or internet registration required.
3.) If you so choose, you can play games from disc, download them from the digital store or remote load them. Sony doesn't mandate any method over the other for multi-format titles.
4.) Just for extra clarification the PlayStation 4 does not and will not require a constant always-on internet connection.