Roth 401(k) and Roth IRA Contribution Limits

Let's say an employee makes $10,000 a year. He is not catch up eligible and he decides to contribute $9,000 as Roth in the 401(k) plan. He also would like to contribute $6,000 to a Roth IRA.

Since the 401k and Roth IRA contribution limits are separate, I believe this scenario is fine (even though he's contributing more than his total income for the year into the 401(k) and Roth IRA combined).

Do you agree?

I don't see a problem with it.

I agree.  Roth elective deferrals in the 401(k) plan are subject to a limit of the lesser of compensation and the annual deferral limit, so the employee can defer up to $10,000 (paying payroll taxes is a whole other topic).  The contributions to the plan come out of the employee's paycheck.

Contributions to the Roth IRA are subject to the lesser of compensation and the annual IRA contribution limit which has a phase-out depending on adjusted gross income.  The employee does not have a high enough income to be affected by the phase-out, so the employee's IRA limit is $6,500.  The contributions to the IRA can come from any source and is not limited to coming from current compensation.  The employee's compensation is merely a factor in calculating how much can be contributed for a given year. 

The IRS has an interesting example at https://www.irs.gov/retirement-plans/plan-participant-employee/retirement-topics-ira-contribution-limits.  Example 1 says the IRA contribution for the individual can be made by the individual's grandmother.