Can I sue the broker I transport people for

Anybody can sue anybody for anything, but it doesn't sound to me like you have much of a case, unless the broker required you to use UPS, or has an agreement with you (which could possibly be implied from previous conduct) that it will accept copied logs where the originals have been lost.  If you could have personally delivered the logs, and chose to take the risk of using a delivery service, I don't think you can impose that risk on the broker.  It is even possible that the broker is required to have original logs to get its own payment from medicaid, in which case why would it pay you when it couldn't get paid itself? You may have a better claim against UPS, but it is likely that your contract with UPS limits its liability in these instances to a minimal sum.  Your best shot would be if you insured the contents of your package, but if not I don't think you have much of a claim.