I suspect the real reason it was acceptable to call in the military is because fairly high numbers of people had already died (and thousands were injured and the property damage was very high). Killing a few more to actually stop it becomes more palatable in the face of something like that.
Excerpt from the wikipedia article:
Fifty-three people died during the riots[24] with as many as 2,000 people injured. Estimates of the material losses vary between about $800 million and $1 billion. Approximately 3,600 fires were set, destroying 1,100 buildings, with fire calls coming once every minute at some points. Widespread looting also occurred. Stores owned by Korean and other Asian immigrants were widely targeted,[25] although stores owned by Caucasians and African Americans were targeted by rioters as well.
And it indicates Hispanics likely played a larger role than blacks:
Half of all riot arrestees and more than a third of those killed during the violence were Hispanic.