Braniff is correct. Here is their schedule in July, 1977:

BN 401 leaves DTW 0800 for DFW and IAH, with a 727-100

BN 400 arrives DTW 1233 from DFW and MCI, with a 727-200, and leaves at 1310 for MCI and DFW as BN 403.

BN 402 arrives DTW 1630 from IAH and DFW, with a 727-200, and leaves at 1715 for MCI and DFW as BN 405

BN 406 arrives DTW 2138 from IAH, DFW, and MCI, with a 727-100, and remains overnight.

Although Braniff had only six flights to / from DTW in 1977, these six flights were the ONLY Braniff flights in the 400 series. Although many airlines dedicate a block of flight numbers to a specific region (most of AA's flights in the 600 series were to / from the Caribbean, most Pan Am / United flighs in the 800 series were to / from Asia or Australia, and most Braniff / EA / AA flights in the 900 series were to / from South America, for example), it's pretty unusual for an airline to dedicate an entire block of flight numbers to a city where they had a small presence.