No, it is not true. You have to pay Social Security taxes on income earned regardless of your age.
Social Security benefits paid are taxable depending on the amount of other income reported on a tax return. Just because one spouse received SS benefits does not mean you need to file differently. You would still want to file a Married Filing Jointly. For tax purposes it is in your best interest to file jointly versus separately.
Up to 85% of Social Security Retirement/Disability/Survivors benefits becomes taxable when all your other income plus 1/2 your social security reaches:
- Married Filing Jointly - $32,000
- Single or Head of Household - $25,000
- Married Filing Separately - 0
