The 'earned income' statement in the TurboTax blog post is referring to the requirement that you must have at least as much earned income as you plan to contribute in order to make a contribution to a Roth IRA. That is not the same thing as the Modified Adjusted Gross Income (MAGI) that is used to determine if your income is too high to make a contribution.
With regard to the MAGI used for Roth contribution limits, rental income does count in this calculation since the starting point is the AGI shown on Form 1040 line 11.
See the following information from the IRS to learn how the MAGI is calculated for Roth IRA contribution limit purposes:
Worksheet 2-1. Modified Adjusted Gross Income for Roth IRA Purposes
@Woggly
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