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Can anyone help me to wrap my head around an explanation of counterfeiting that I think is incorrect?

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I have the hand on the left and I thought I could play the A2 for the low pot. The other players at the table told me that since there was a 2 on the board it counterfeited my 2s and I had no qualifying low hand.

This is contrary to my understanding of counterfeiting. Who is correct?

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You would use [A2][543] and the villain would use [A5][432] to make the same Lo. There is no counterfeiting here.

If the board was instead K324J, you would have no Lo.

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