Inspections take place to provide customers with very detailed information about a car, including a written report and anywhere from 100 - 300 photos. This is an excellent way to get a good idea of the condition of a vehicle and most customers are very happy with how much they have to make a decision on if they want to buy that particular vehicle after this step. These style of inspections are for vehicles with a used car dealer or are being sold privately, and differ from the inspections for auction vehicles.
J-Spec has a network of mechanics and trade-related people throughout Japan who can go and look at cars when an unbiased opinion is needed and when we want very detailed photos and info about a car. Inspectors often have to travel for several hours (possibly by public transport given how congested the cities are) so they normally cannot bring tools or equipment with them to where the car is going to be inspected. As a result invasive inspections that require workshop tools (compression testing, measuring brake rotors, etc) are not possible, nor is full access to the underside via a hoist unless the seller of the car has one. Think of an inspection as though you were looking at a car which is for sale privately, and have a mechanic come along to look at the car with you. They will be knowledgable about vehicles, will know what to look for and will do as much observation and testing as is possible given these constraints.
Inspectors will test drive a car where possible, but if a car is not registered then it will be driven at lower speeds in the parking area to learn as much as possible. Inspectors are paid for their time and transportation regardless of if the car is purchased or not, so this ensures there is no bias or that they have a vested interest in the outcome of the inspection... they will simply tell us what the car is like.
History suggests customers usually choose to buy cars about 90% of the time based on the results of the inspection. In cases where cars have not been purchased it may be due to the car having a major problem we weren't previously aware of (engine problems, previous accident history), or may be because the car is not up the same standard we had hoped for based on what the seller told us about it initially.