While the treasure may 'belong to The Crown', the finders/landowners will be paid a fair market value if it is retained for a museum etc.
If the museums don't want it it is returned to the finders/landowners to keep or sell on.
The finders mentioned in the report appear to have been trying to circumvent these rules. Hence not reporting the find, and possibly denying archaeologists the chance to follow-up on the find. Also (more likely the intent) not advising the landowner on whose property it was found and so not having to pay out a share of the proceeds.