Could be but surely he can multi-task. Why not charge on with the school records like he hinted about before the big silence.
School records don't directly prove ineligibility and can be protected by privacy in a way that birth records cannot, IMO.
Trump was acting as though nonexistence of an HI Obama BC was a certainty. That was Trump's Ace in the hole. That is what emboldened him, IMO, but he got trumped or appeared to be trumped. Without his “Ace” he was properly deflated until and unless a BC forgery can be proved in the court of public opinion, and he had no choice but to back off.