A scooter is quite rigid for its weight and size, and there shouldn't happen much more than some scratches, broken mirrors etc.
There are just two issues I can think of:
- If the scooter fell hard on a brake lever, this could have damaged the lever itself or for example one of the gaskets inside, when it's a hydraulic brake. Obvious signs would be a brake fluid leakage, usually at the lever or at the brake, or when you can just pull the lever onto the grip. At least, you should be able to say if the scooter acually did fell on the lever from the scratches. If not, don't worry.
- Liquids. It's clear that oil and fuel could have leaked out, which is a mess, but usually not really a problem, except it got on the brakes. This can also lead to some starting problems, but that's it. But most scooters still have an old style, not sealed battery, which could have leaked. The acid is typically dumped to the street through a hose, so no problem for the scooter. But it's now missing in the battery, and you can't simply top it up with distilled water. I'd suggest you inspect the battery and the acid levels.
However, liquids leak out slowly, so if the scooter was tipped over and put up directly after, this shouldn't be an issue.
Your last question is a legal one and can't be answered without knowing the country, and this is also not the right place for it. But in general, an inspection is the first step of an repair, so it sounds reasonable that the guy has to pay for it.