The case was "strange" but police would get to the bottom of it, he said.
"It's certainly a wee bit unusual in the circumstances - I mean, most people do their business dealings by day, and do it legitimately with receipts and changes of ownership, but none of that happened either.
"It was certainly a wee bit strange for us, but we're getting to the bottom of it anyway."
Mr White said police were not considering charges over the car swap, which was a civil rather than criminal matter, but charges could be laid over the altercation.
No physical assault had taken place, but brandishing a weapon could still be a technical assault.
Mr White said police had spoken to a number of people and the investigation was ongoing.
A decision on any charges was likely later in the week.