Not affiliated with the US Social Security Administration
I haven't seen much regarding procedure with error-in-fact cases, but yes, in my opinion SSA should consider potential errors-in-fact when reviewing applications.
Note there is an appeal process if the determination is against you. I have seen the appeal process mostly in the context of disability determinations, but here is one relevant document :
Depending on the difference in benefits, you may want to seek (legal) representation to help you. Many representatives (lawyers) will work on a contingency basis so they don't receive fees until you win your case.
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