DP is a catch-all term for two different stages in the process. I presume Cambridge have merged the two because applicants were working themselves up into a lather about it, making incorrect assumptions and pestering the PAO.
The first step under DP is that offers are assessed by the Degree Committee. The issue here is that the process is not necessarily tied to Degree Committee dates, which applicants obsessed over. At this stage the Degree Committee (or a subset of members) review the quality of applications across all the degree programmes they run. If they are perhaps trying to improve the quality of one programme, or they find the quality of applications to one programme is especially high one year, and another lower, they make the strategic decisions about being tougher on offers or viring numbers between courses. That's when people who have got a DP flag might still get rejected.
The second step is at PAO where a final check of the application is made to make sure the is not error or fraud in the application. Because PAO have to check every single offer in detail (and you can't just hire in temp staff with the level of knowledge and accuracy needed) this process tends to get extremely jammed up from the middle of March and the delays can be several weeks. However, it's very rare to get a rejection from this stage, you basically have to have made a fraudulent application, or come from a new university in a jurisdiction with poor academic standards/monitoring.
So DP can last anywhere between a few days or a few months, depending on where you hit the cycle of those two phases. The chances of a rejection if you get to DP I'd say are less than 10% though.