Not true.
I've seen a tournament stopped from rain. There was not a second of thunder or lightning. But it was raining so hard, you couldn't see 50 feet in front of you.
Also sometimes it's not safe in the rain depending on the course. Like Renny in Charlotte. That place is just not safe to play when it's raining.
Or RL Smith after a heavy rain. Those rivers can flood over their banks in a flash flood scenario even if it is sunny after the rain stops.