There is some contradiction between ESTA and the US Embassy with regards to arrests and convictions.
The ESTA form asks if you have ever been convicted of a Crime Involving Moral Turpitude (CIMT) or involving drugs. If you can tick no, you should be able to travel using ESTA, even if you've been arrested.
The US Embassy states that if you have ever been arrested, even if not charged, you are ineligible for ESTA. End of story.
I have a drink driving conviction (which is not a CIMT). When I applied for my US student visa I was told I was ineligible for ESTA and must apply for a visitor visa for the US in future.
When I got a visitor visa later on and travelled to the US the immigration officer at the airport told me I didn't need a visa and could travel on ESTA because drink driving wasn't serious enough to need a visa.
So as you can see, it's not set in stone. It depends on the nature and seriousness of the conviction. I have successfully lived in the US and visited a further 5 times (and will be visiting again in September) since my arrest and conviction.
But to be on the safe side (and because US immigration is aware of my conviction) I will be applying for visas to visit the US for the rest of my life. Whether I really need them or not though, is still up for debate.
As someone who has been in the position of having a conviction I would urge her son to be aware of the repercussions of having one. I am currently banned from entering Canada because drink driving is a felony there. I will also need a visa to visit Australia because I have a conviction... And those are just the countries I know about.