The 1st FG may be another possibility, see this MACR:
https://catalog.archives.gov/id/91069235
The MACR is for P-38 43-28815 flown by Richard P Decker, 72st FS, 1st FG. The MACRs says he was on an escort mission to Munich when lost. The Munich mission that day was for an aircraft engine factory located in Allach (Munich). Dachau is about a mile north of Allach.
One thing odd about this event is the fact that while low level strafing by escort fighters was often done on the return flight from bomber escort missions, they usually would be some distance away from the bombing target before they would do such an attack (often on railroad targets).