The FAA says that, specifically the 7110.65 which governs ATC rules and procedures. In a radar environment it allows for departures when the arriving aircraft is 2+ miles from the runway, and there will be at least 3 miles of separation within 1 min of takeoff. A separate rule requires that the departing aircraft is at least 6000ft down the runway and airborne before the arrival crosses the runway threshold.
If there is a departing plane rolling up to the hold short line and confirmed ready for immediate takeoff, there is possibly time to get them out and maintain separation. If it's low visibility, the departing plane is rolling slowly and not confirmed ready, then it's a bad bad idea.