Well firstly there's no real evidence Jill was being 'stalked' or on the receiving end of any persistent unwanted behaviour.
According to her fiancee, Alan Farthing, her greatest concern was leaving the BBC studios late at night/early morning and having to then walk to her car.
According to her cousin, Judith Dando, from time to time she did receive some unwelcome attention but it was never considered a real issue and Judith was unable to recall anything of any detail.
No one was seen hanging around Alan Farthing's home in Chiswick where she lived at the time. Nor was anyone seen hanging around the BBC studios or 29 Gowan Ave which at the time of her murder was little more than a storage facility and postal address for mail.
Police went through her diaries and found nothing of any concern. They also went through her fan mail and whilst some was considered 'odd' there was nothing to suggest the 'odd' mail was originating from any one fan.
As far as I can see there's not a shred of evidence to suggest any particular individual was obsessed/stalking Jill or causing her any concerns about her personal security. But John Lennon may well have thought the same.