It's understandable that you recall it that way, because it is the type of too-good-to-be-true, hate-Whitey lie that the mainstream media lives for. A "fact too good to check," as some reporters describe such tales.
The following is from a dispassionate account of the incident, found here. It paints an accurate picture of the characters who dominated the culture in Mayor David Dinkins's New York, where I lived at the time. It is worth quoting at length:
"The most conspicuous anti-Semite plying his trade in the summer of 1991 was [City College professor Leonard] Jeffries, whose relentless slurs against Jews enjoyed enormous attention in the press during the first weeks of August. When he was criticized, many mainstream blacks rushed to Jeffries’s defense or kept silent.
"Black newspapers like the Amsterdam News and the City Sun; the black radio station WLIB, long an open-air forum for anti-Semitic ranters; and some of the black activists who would later figure significantly in Crown Heights—Al Sharpton, Colin Moore, C. Vernon Mason, Sonny Carson, Lenora Fulani—all went to bat, expressing their approval of Jeffries’s “scholarship” and denouncing his critics as race baiters. This, then, was the immediate background to the riot.
"Not only was anti-Semitism in the ether, it was gathering steam as a loud and increasingly mainstream black movement when a station wagon from the entourage of Menahem Schneerson, the Lubavitcher rebbe, careered out of control and crashed onto a Crown Heights sidewalk on the night of August 19, crushing to death a black child, seven-year-old Gavin Cato, and leaving his seven-year-old cousin, Angela Cato, badly injured.
"The violence erupted immediately. When the driver of the station wagon, Yosef Lifsh, stepped out of his car with the intention of helping the children he had hit, he was set upon by angry black bystanders who beat and robbed him before the police could reach the scene.
"Moments later, an ambulance from the Jewish-run Hatzolah service arrived. Police, seeking to remove the object of the crowd’s anger, directed the crew to take away Lifsh and his passengers. Before the Hatzolah vehicle was out of sight a city ambulance had arrived to begin the gory and laborious task of removing the Cato children from beneath the car, but Lifsh’s attackers were enraged at the decision to place him in the first ambulance."
Immediately after this, a mob began smashing car windows, and seized a passing Hasid from Australia, Yankel Rosenbaum, and beat him—some of them yelling "Kill the Jew!" One of the crowd, Lemrick Nelson, Jr., stabbed him to death.
"Racism" is an ideological and vacuous word in most uses, but if anything qualifies as racism, I'd say that does.