Usually (but not always) higher quality stainless steel is not magnetic, while the lower quality is slightly magnetic.
However even slightly magnetic can be a problem in an MRI - and worse, there is no practical way for the MRI tech to tell how the stainless steel will act, so they will err on the side of caution.
I just noticed that my own "iron" ring (which is stainless steel) doesn't seem to respond to typical magnets you'd find around the office.
Clearly _iron_ is though, considering it's the element with the symbol "Fe" which is short for Ferrum.