"the IRS website says you don't need earned income as a condition to claim the saving's credit"
It's doubtful that it says that anywhere. It's likely that it says nothing about needing earned income and saying nothing about needing earned income is not the same as saying no earned income is required.
A prerequisite to claiming this credit is making a retirement contribution that you are eligible to make. A prerequisite to making a retirement contribution is having compensation (earned income). Therefore, having compensation is a prerequisite to claiming this credit. A requires B and B requires C, therefore A requires C. (To be a Catch-22 there would have to be contradictory requirements, and that's not the case.)
