As a matter of fact, "Die on error" or "Reject" option is available on DB output component not DB Input component.
For tFileInputXXX components(tFileInputDelimited), there is processing of string to object. That's the reason why the rejects row is available in tFileInputXXX components.
Rejects row link gathers the data that does NOT match the filter or are not valid for the expected output. This link allows you to track the data that could not be processed for any reason (wrong type, undefined null value, etc)
But for t<DB>Input components, you can read data stucture from known table stucture(Restrieve table schema). There is no processing of String to object. So "Rejects" is available in t<DB>output component to avoid table struct conflict between source DB and target DB,etc.