The Nikon Coolpix P610 and Filters. What size and if at all?

Search as I might I could not find the filter size for the Nikon P610 in the manual. So I looked online and uncovered a whole can of worms. Somebody had enquired of Nikon the same question but had been told the P610 would not take filters, that the grooves inside the lens mount were not threaded and that any filter would only be lodged there and would fall out. Then somebody else stated that their 52 mm filter fitted fine.

Having a 52 mm filter in my hand (see previous post) I tried it on the P610. It fits perfectly. Firm as a rock. No problem at all. Here I am trying and failing to dislodge the filter other than by unscrewing it:

Problem solved but what were Nikon thinking of when they produced the camera and the manual?