I was trying to do the reader's digest version.
But since you ask: At the same time Mr. Chop Shop is physicaly swapping his VINs, he is either "manually" revising the paper title with some white-out or "washing" it through another state where they don't brand titles as salvage. Now he has a fresh, unbranded title to sell the car with. This also adds a plethora of additional Federal felonies: Mail Fraud, Wire Fraud, Securities Fraud (titles are considered a "security instrument") and ITSMV -Interstate Transportation of Stolen Motor Vehicles.
Students, your final exam will be next Tuesday.