Is my 1943 roosevelt dime counterfeit?

An appraiser said it is worthless because it has to be a counterfeit. This is unlikely because it belonged to my grandfather who lived in a tiny house on the edge of a ranch where he worked. I doubt he had the space or knowledge to produce counterfeit coins. If anyone could let me know where they get their own coins appraised, I would like to take mine there to get an accurate value on it before I list it on ebay.

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