I always read it (not that I need one) that you need "a" license for the et you will be running, and either NHRA or IHRA would be accepted. The DW rules have no "track sanctioning body" stipulation attached.
All vehicles must meet NHRA safety rules for the e.t. and speed they are capable of, and drivers must be IHRA or NHRA licensed if required. Drag Week officials will not accept time slips that are quicker or faster than the cars techd legal e.t. and mph. Running quicker than the safety equipment allows is cause for disqualification at the discretion of the race director.