Marion King, 44, gave a statement to detectives in which she said Miss Doyle told her a man driving a blue car had repeatedly asked her to get into his vehicle.
The High Court in Edinburgh heard Miss Doyle told her friend that she refused and "ran" towards her home in Greenock.
Mrs King, of Greenock, was giving evidence at the trial of John Docherty, 49, of Dunoon, who denies murdering Elaine in Greenock in June 1986.
Mrs King told Donald Findlay, defence QC, she gave a statement to officers hours after Miss Doyle's body was discovered on June 2, 1986.
The court heard that in the statement she told officers she had known Elaine Doyle for two years. Mrs King also told detectives that before she had died, Elaine had told her about an incident that happened about a month earlier.
The court heard Miss Doyle felt she had been "pestered" by a man driving the blue car, which was possibly a Marina model.
Marion told officers Miss Doyle said the man asked her to get into his vehicle - but she refused and continued to walk on. The court heard the man continued to drive on beside her. He then asked Elaine to get in for a second time, but she refused and "ran" home.
When Mr Findlay asked Mrs King whether she thought Miss Doyle had made the story up, Mrs King replied: "No."
Mrs King also told detectives in her statement that Elaine thought the motorist looked "tall" and had curly hair that had looked as if it had been permed.
The trial continues.