A step child is from a legal marriage. Nothing harassing about seeking proof.
Some people don't do obituaries or may not list kids at all.
This is clearly a biological parent since the OP mentioned the child support settlement
There is nothing in the contract that says documentation is required. There is privacy issues with that, some low level sup at UPS is not entitled to view employee birth certificates, family history, court orders ETC.
Unless this emoyee is claiming their father died twice or something like that there is no reason to suspect fraud. Just pay the two days and move on. If there is reason to suspect fraud then the manager should get loss prevention involved and have a steward present.