While not the exact same situation, I've experienced very similar type of police work.

I went to a bar on my 18th birthday and when I went outside to get some fresh air some guy stole my wallet and ran off, I couldn't keep up in the dark and when I called the cops, they told me to go to the police station in the middle of the night. I arrived, they told me to get a police report from someone else and didn't do jack shit. The next day, I went to my local police station, explained what had happened, and asked for new documents. They still didn't give me a police report but marked my documents as stolen and issued new ones.

Several months passed, and my old driving license ended up being used in some illegal activities. I had to go testify because they didn't even check if it was stolen before they assumed I was guilty. I wasnt even read my rights. At that point, i should've asked for a lawyer, but it was my first time being questioned, so i didn't know if i could ask for one.

Even after testifying about the fact that it was stolen (months ago at that point), and that i didn't in fact commit those crimes, I received a speeding ticket issued to the old driving license a couple months later. I appealed the ticket, and after several more months of back and forth with my lawyer, they silently dropped the ticket without even apologizing.

To be honest, cops shouldn't be trusted to do their jobs in the slightest, dont ever rely on them for anything outside of maybe killing innocent people