If your car is stolen, it's reasonable that your Google docs are read?
- they have no evidence they ever had a car
- bank records do not show evidence of any purchases of a car or insurance
- registration records do not support the person had a car registered to them
The yes the police will probably start investigating them for fraud as they do many of thousands of times are year, and they may well seek forensic computer evidence.
I'm squicked out about the invasion like many are, and if I thought about it carefully I expect I would come out against the idea, but I can actually see the case for this invasion.
In that case, they are being investigated as suspects and should obtain all of the due process that suspects are afforded under the law. Reasonable suspicion, warrants, etc. should all be obtained - not "we won't investigate the crime unless you surrender your rights and permit us to investigate you as a suspect without warrant or cause."