I am reminded of the 'sightings' that happened at Gatwick (I believe), a while back.
Do I think the airport operators would shut down without reasonable evidence? Possibly, yes. If I were in a restaurant with my family and the fire alarm went off, I would not wait for proof of a fire, I would leave immediately because the repercussions of being wrong and waiting too long would be of a magnitude that warrants it.
If I were in charge and got a 'report' of a drone over a runway I probably would have diverted flights as well. Are these pilots that are seeing something on approach, and possibly misidentifying as a drone? Perhaps. Well then the report can at least say that. But the way that report reads, it leaves almost no doubt that there were drones over or near runways on 2 occasions.