Golenbock's details are a little off, perhaps forgiveable in the pre-internet age when it wasn't so easy to track down data, but here's how Reiser's SABR bio explains the situation:
On July 18, 1942 the Dodgers had an eight game lead over the Cardinals when they went to St. Louis for a four game series. Reiser, batting .356, was riding an eleven-game hit streak. In the eleventh inning of a 6–6 tie on the July 19, Enos Slaughter belted a long drive off Johnny Allen. Reiser raced toward the center-field wall, narrowly avoiding the flagpole that rose from the playing field, and caught Slaughter’s hit in full stride—and then hit the concrete wall an instant later. The ball fell from his glove and, although dazed, he threw the ball to the cutoff man, Reese. By the time Reese fired the ball home, Slaughter had circled the bases to win the game.
All attention turned to number 27, who lay on the field motionless, facing the sky, his shoulder separated and blood trickling from his ears. When Durocher reached him, the manager started to cry. Pete was carried off on a stretcher and woke up the next morning in the hospital with a fractured skull and a brain injury. The Cardinals’ team doctor examined him and recommended that he not return to the field that season. In the era before the effects of a concussion were fully understood, Reiser did what gamers do—he returned to the diamond as soon as he could walk. He was dizzy, had a hard time focusing, and felt weak, but there was no keeping him out of the lineup.
He would never be the same player again.
Reiser hit .244 from July 25, the day he returned, to the end of the season, even trying to switch-hit to minimize the pain in his shoulder. The Dodgers’ lead evaporated down the stretch as St. Louis edged Brooklyn by two games. From the heights of July, Reiser ended up batting .310, but still led the league with twenty steals. Before the injury, teammate Billy Herman—who had played with Hall of Famers Chuck Klein and Hack Wilson—said Pete Reiser was the greatest player he had ever seen on a baseball field.