We're told Lindsay and the alleged victim -- Thaer Kamal -- have both refused to sit down with the detectives for an interview. Important to note ... neither has an obligation to sit for an interview, but it's unlikely cops will even refer the matter to prosecutors if the alleged victim is uncooperative.

But it gets way more interesting ... Sources tell us an investigator from an insurance company contacted Lindsay's lawyer and said they were investigating the alleged victim for 6 - 8 cases of insurance fraud -- allegedly staging car accidents and filing phony claims.

And the plot thickens ... although the insurance investigator told Lindsay's lawyer he believed the person accusing Lindsay of hit-and-run was the same person they were investigating ... sources at the insurance company tell us the alleged fraudster's first name is Amr -- not Thaer, and the last name is different as well.

We do not know if Thaer -- a former soldier in Iraq -- used such an alias.

But we do know that Thaer has hired famed lawyer Mark Geragos, who has already made a settlement demand to Lindsay. We contacted Geragos about the allegations and he said his guy was not involved in insurance fraud, but when we called back regarding the alias Geragos did not pick up.

And the final twist -- Lindsay is in court next week for her final probation progress hearing. If the hit-and-run case goes haywire on her, it could jeopardize her freedom.