If I showed someone else's US birth certificate to an immigration officer but then said it wasn't mine, am I still eligible for a green card?

Question Details: I came illegally 11 years ago. At the airport an officer asked for my ID, I showed him the birth certificate and said, "I can check this - do you still want to say it's yours?" I said it wasn't, was fingerprinted, had my information put in the computer and driven back voluntarily to Mexico. I came back again 2 days later.

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