The event that shows that your project has finished changes nothing except for your own char. Other chars have to determine in their own minds whether or not your char has a right to what your char picked up, or if your char is a lying thief. They still have to make that same determination even if your char states from the events page. The only "evidence" that can really be confirmed is what everyone saw, which is your char picking things up.
Your char "proves" it by being convincing, and hopes that those with uh-tho-ri-tuh are well convinced

. I've never yet had a situation where my chars could not successfully convince others, and I've never used the exact events as "evidence."
IMO, authoritative people in a well organized town should know who has rights to resources before it gets to the point when someone is picking them up. It requires little effort, and lets those with authority have a bit of fun when someone is bold enough to claim something they really didn't work for. If your char is in a position of authority, why would he or she be making an ass of himself or herself by obviously not knowing what's going on in his or her town?
By the same token, if a char doesn't take any of a few simple possible measures to protect his or her property "rights" regarding abandoned projects, then perhaps becoming a victim of the system will do alot to teach the char to do so in the future.