That depends. Can your unique part number allow you to trace the part all the way back to the raw material? I don't think that it is a regulatory requirement, but traceability back through the entire supply chain is. What specifically does your CSR's say about traceability requirements for critical components?
The goal of traceability is being able to track a part all the way back through the supply chain to the raw material. From your example, if your customer contacted you with a material related failure, could you take the stamped information and track it back to a specific batch/heat of steel? If you can't do that, then the amount of potential risk the company can be exposed to increases substantially - especially if there is a recall situation. How confident is the company, that should there be a problem, the raw material can be identified and then followed back up through the chain to identify any other possible suspect finished goods?
Hope this helps!