Unfortunately, you're not correct. The Criminal Justice Act 1972 updated the definition of a public place to be:
The pertinent bit there is have or are permitted to have access which does include any private land to which any member of the public has been permitted to have access at the relevant time. So in the stately home example, Blaser243 is quite correct to state that the home becomes "a public place" for the duration that the public are permitted to have access, at least as far as the CJA is concerned. It reverts to being a private place once the permission for the public to enter has been withdrawn.
As for the rest of the story and the actions of the Police - this to me is either connected to some other activity that has caught their attention or is the result of someone very overzealous looking to make a name for themselves somehow. I strongly suspect it is the former rather than the latter...