So for other reasons it's important for you to file the accident report: if you continue having problems with your finger or hand and need to seek medical attention for it, you will want to be able to prove this was a work related injury. If you don't file the accident report, you will have no recourse in the future. It has nothing to do with changing how they do business or anything, it's about protecting yourself in the case you need to go to court.

Demand to fill out the accident report and get a signed copy for your records.

Good luck,
seesaw