That's not supported by the numbers.
Actually, he's quite right, except that whites didn't race riot in their own neighborhoods, they invaded black neighborhoods and killed blacks there.
http://en.wikipedia.org/wiki/Rosewood_massacre
http://en.wikipedia.org/wiki/Perry_race_riot
http://en.wikipedia.org/wiki/Tulsa_race_riot
http://en.wikipedia.org/wiki/Chicago_Race_Riot_of_1919
http://en.wikipedia.org/wiki/Detroit_Race_Riot_(1943)
http://en.wikipedia.org/wiki/Knoxville_Riot_of_1919
http://en.wikipedia.org/wiki/Elaine_Race_Riot
There are quite a few more. Up to the 50s race riots consisted largely, though not always exclusively, of whites attacking blacks. Since then, they've consisted almost exclusively of blacks attacking whites and each other.
For some obscure reason, in the "modern race riot" blacks almost never leave their own neighborhoods and attack their "enemies." They stay in their own areas and tear them up.
The first "modern race riot" was in Harlem in 1935.
http://en.wikipedia.org/wiki/Harlem_Riot_of_1935