There is no option to claim a stimulus payment on the 2022 tax return. So I don't see an option for your parents to file a joint return as your dependents in the scenario you describe since there is no withholding. They each need to file a separate married return and indicate they can be claimed as a dependent on someone's return (Yours).
You are correct the nontaxable social security does not count toward the gross income test ($4400). However it does count as part of the 1/2 support test and the head of household test for providing more than 1/2 the cost of keeping up their home.
You are correct filing as dependent with no earned income is going to limit their standard deduction and likely produce a tax owed for each. I assume you have done the math and claiming them results in a positive net for the family.
Of course the net would be greater if they did not file tax returns since there is not a filing requirement or refund reason to file.
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