Roth IRA for a minor

I have read that a minor can have a Roth IRA as long as they have ANY type of job that pays them cash - for example babysitting, paper route, ect... It seems this is a "scouts honor" type of rule where the maximum that can go into the Roth IRA is what the minor has earned or claims to have earned.  Follow up - because they are saying they have "earned income" does that then mean they need to be claiming that income from babysitting, ect....