''the airport is below operational minimums and we have elected to divert'' is OK if talking to those in the know. But for PAX
"Closed" is as close to the truth as they need.
Had an aborted takeoff happened, and the plane went off the end of the runway, this action of "checking" the runway would have been on more arrow in the quiver of this pilot's defense .
Or a rope to hang him - depending on the circumstances.