I don't think they were the source of the leak. The reason Scobie replied so quickly after the story dropped was because the Sun would have contacted both BP and Team Sussex before going to print. Rather than confirm the story to the Sun, they chose to have Scobie stir the pot.

The reason I don't think they are the source is because they need for people to consider them still part of the royal family. That connection is the only reason people hire them. They would have wanted to hide this news for as long as possible in the hopes of Charles changing his mind or offering them another property. Since Charles had extended the deadline until after the Coronation, this would have been the perfect story to drop then. Which could be why Team Charles wanted to get the news out now.