Sorry 'minor' doesn't hack it. The test is whether it is moral turpitude* or not, which is not at all the same thing. (*or drug related or a war crime, or being a commie or a fascist all of which are probably moral turpitude in US eyes anyway)
'Fighting' is not normally moral turpitude.
So if he ticks the NO box on the ESTA form he will be telling the truth and should get in, no problems. He should also remember to tick the NO box on the green form on the plane.
And no, the US authorities do not have access to every minor criminal record in the UK. Terrorists yes, sex offenders probably, anyone bad enough to get on interpol's list, yes.