"With full Social Security client is not eligible but none of her Social Security is taxable."

You might be mixing provisions.

"Which is it?"

Did you follow that link to the IRS? They know everything.

"Earned income does not include:

• Pay you got for work when you were an inmate in a penal institution
• Interest and dividends
• Pensions or annuities
• Social Security
• Unemployment benefits
• Alimony
• Child support"