You could look under the deck with a bright light and a mirror for signs of having cut some grass.
Even if they fastidiously washed off the deck underneath I doubt they would have repainted it, so look closely for scratches that inevitably happen when stones and twigs hit it.
As to the hour meter, to my knowledge, leaving the key in the ON position keeps the hour meter running. Nothing in the circuitry to sense when the engine is actually running or not.
It is presumed that if the key is on, the engine is (or should be) running.
If anything in your warrant language specifies an expiration based on a certain number of hours, you might want to have the dealer give you a signed affidavit stated the warranty will expire at (adjusted hour reading) instead of the arbitrary factory expiration point.
I hate insinuations like "yeah", the dang thing was a couple of miles/hours out of warranty so I had to pay for it.

If you trust the dealer and believe you had bought the right machine for you- 3 hours is a drop in the bucket. Sometimes a PDI is textbook, sometimes a tech needs to take time with the tractor to get things right. Even if he took it to Sally Jone's house to have her drive it on her lot for a test drive- what is the harm? You've never bought a new car w/ 0 miles on the clock. If you don't believe the dealer is someone you can build a relationship with- then walk away.