I've now had three of these, and remember years ago taking the adaptor off the deck and 'adjusting' the record so that it played true.

 I've heard it many times at venues, and always seem to notice when it was wonky ?.... Do all copies play off centre?

Not mine.

Nor mine.

Hmmm, many thanks 

Counterfeit copies of The Righteous Brothers 45 exist. The few I have seen have Verve issue labels and are off centre.