Could someone tweak the image? Of course. But as a practical concern, probably less than 20 people have the image manipulation skill it would take to do something like this in the ~20 minute handoff period. The transporters certainly don't. This is a bullshit argument, and you know it. And these pictures are not just of the odometer, but the entire car, including the VIN. Photoshopping all of this believably would cost you more than just paying the damages on a joyride. It's a non-issue.
And I think you're misunderstanding something: the issue is not the time before the transporter get custody of the cars, but the many days that the cars are in transit cross-country. If the timestamp didn't exist at the time the transporter starts their journey, the next handoff knows something is up.
As for already trusting us, our clients do, yes, but the point of this solution is to increase the trust-level of custodianship handoff between people who are not our clients. A blockchain is a great solution for this, and a database is simply an inferior solution. And NO, they don't have to trust us to "push the right data on-chain". This logic runs in a very simple SPA and is immediately verifiable on-chain, without using our software, because the blockchain's global state is open.