Did smugglers or sheep give name?

In a recent article, published under the heading ‘A nursery rhyme hides the wretched secrets of New England Bank’, the Observer said that it is popularly accepted that the area of West Marina known as Bopeep derived its name from the hide-and-seek proceedings of smugglers, who were very active in the then very thinly populated district, as in the old nursery rhyme, Little Bo-Peep.

However, according to the Kent Rail web site, the name ‘Bopeep’ was taken from that of the nearby inn, mentioned in the article, which in turn acquired the title as a result of local sheep herding.

Does anyone reading this know who is right? Was it smugglers or sheep?