It's not actually true.
Fighting is presumably assault and is not a crime of moral turpitude (which would actually debar you from using the visa waiver scheme - and possibly from getting a visa as well.)
The US Embassy play this very cannily - they say you MAY be ineligible to travel and need a visa - which is true. To find out through them whether you do need a visa or not you have to apply for one. And once you have applied for one they will grant it rather than tell you you didn't need to apply.
This is frequently discussed in the travel section - suggest you browse through there.