The Australian reported that he had been abducted from a wine bar on 17 January after missing the cut at the Sony Open in Honolulu the previous day.
Allenby, 43, says he cannot remember a two-and-a-half-hour period from the night when he suffered facial injuries.
But he said: "My story stays exactly the same as the way I told it."
Allenby has said that a homeless woman spotted him being dumped from a car several miles away from his alleged abduction.
However, US press reports later claimed the woman had given conflicting details, saying she found Allenby just one block away from the bar he had been drinking in.
Allenby, who is preparing for the Phoenix Open starting on Thursday, admits there has been "a lot of confusion" about the incident.
The four-time PGA Tour winner said: "I never lied to anyone.
"From about 23:06 to about 01:27, I have no memory in my brain. I have nothing.
"I can't tell you how frustrating that is because we all want to know the truth, we all want to get to the bottom of it.
"But there's no way in the world what I drank could do what was done to me, not a chance in the world."
Golfer Robert Allenby says police are continuing to investigate his claim that he was kidnapped, robbed, beaten and dumped in a park in Hawaii.