It's an interesting one. Filey is certainly in Bilsdale's official service area, but then so are York and Harrogate which are very definitely considered to be Emley territory for editorial purposes.
http://tx.mb21.co.uk/gallery/bilsdale/maps.php
Looking at various maps and coverage predictors it seems that the people of Filey have a choice of all three Look North services, from Bilsdale, Hunmanby and Oliver's Mount, and a quick look at Street View suggests that lots of households have multiple aerials for that purpose
I suggest that if Sky defaults to Leeds, that is a pretty good indication of the BBC's intention in terms of which region is intended to primarily cover the area. And it makes sense - Filey is part of Scarborough, so local politics are going to be covered on the programme that covers Scarborough.
The anomaly seems to be why Oliver's Mount is a relay of Emley, which seems to be for historical reasons so as to replicate the 405 line service with the old YTV transmitter at Scarborough. It would perhaps make more sense for it to relay Bilsdale these days.