The article's presentation of the James-Stein estimator sets the arbitrary point at the origin. (My previous comments should be read in this context). Of course, we could set it anywhere, including [42,...]. Let's call it p. Regardless of where you set it, the estimator suggests that your best estimate û, of the mean μ, should be nudged a little away from x and towards p.

My point is that the choice of 'p' (or, in the article's presentation, the choice of origin) cannot truly be arbitrary because if it reduces the expected squared difference between μ and û, then it necessarily contains information about μ. If all you truly know about μ is x and σ, then you will have no way to guess in which direction you should even shift your estimate û to reduce that error.

If you do have some additional information about μ, beyond just x alone, then sure, take advantage of it! But then don't call it a paradox.