I am resident alien for 12 years. About 7 years ago, my friend and I were driving cross-country. We accidentally crossed the US border into Canada. My friend turned the vehicle around, but we had to pass the US border for reentry. I was much younger and naive back then and my friend told me just say "Citizen" if asked, which is what I did when border patrol asked. They asked for my ID and I gave them my U.S. drivers license and determined I was not a US citizen and then detained me for questioning. I thoroughly apologized and said I made a really really big mistake. After validating my legal status (I also didnt have my green card), they eventually let me into the US.
Was that a false claim of US Citizenship?
Will that be a problem if I naturalize?
Will that show up on records?