A wrench is a wrench, or is it?

Does anyone know if a TaylorMade wrench will work on a Callaway X Hot Driver?

I was too cheap to buy the driver brand new but managed to snaffle a good deal (with the right shaft) off ebay. However, the club was sold with a TaylorMade wrench which the seller tells me will work just as well.

Has anyone experienced something similar? Are there any implications of using a different wrench?

p.s. I was custom fit for the driver, however I was foolishly not custom fit for the wrench.