In that case, he was not arrested for being unable to pay his bill. He received a summons to court, failed to appear, and so a warrant was issued for his arrest. The $350 was his bail amount, which is funds that must be provided to the court in order to be released while pending trial (you get this money back once you appear before court). He also wasn't convicted of a crime and sentenced to jail in this case, just arrested. He would be "kept" by the courts (if he couldn't post bail) until his court date as a way of being forced to appear.
If a judgement was awarded against him, it still doesn't always mean he has to pay. If someone refuses to pay a judgement (but did show up to court) then typically their wages are garnished, which means the court orders that a certain amount of money be witheldwithheld from income, tax refunds, etc. until the judgement is paid. However, if the person ordered to pay can prove that they would not be able to have sufficient money to survive if they are garnished (I'm not a lawyer so I am unclear as to the exact process/standards) then there is a chance that nothing will be garnished at all.
So in short, no, there is no such thing as debtor's prison in the USA. There is definitely such a thing as being arrested / put in jail for defying court orders, and I'm sure if you took out loans while knowingly being ableknowing you have no ability to repay them that you might be able to be charged with some sort of fraud, but just not being able to pay your bills doesn't mean you can go to jail. Of course, there is very little protecting you from simply running out of money and becoming homeless, but that's not your question.