Yes, they do have to report this.

Takeoff incursions are more dangerous because a jet taking off has few options once it reaches a decision speed. It must take off and can only go in a straight line. A landing jet has a easier time of going around or landing long to avoid the obstacle.

From the OP, there is no way of knowing who is at fault. The UA jet could have been on the wrong runway or misinterpreted a taxi into position and hold for a clearance, the other jet could have misunderstood its clearance to cross the runway, or the tower could have given clearances to both by mistake. Or the tower might have thought the other jet had already crossed when it cleared the UA jet.