Its probably made of 316 stainless, which does contain iron but in very very low amounts. There''s more nickel and titanium in 316 than iron that coupled with the thinness of the needle to begin with would make it next to invisible to a coil or pinpointer.
Cutlery grade stainless, 18/8 or 18/10 is magnetic as its a more than likely a high carbon steel coated with nickel and or chromium so that its not too soft to cut but still has some resistance to rust.
Even the most expensive forged blade professional and sport knives are not impervious to rust. True that they use a Chrome Moly Vanadium steel but will rust if left in a puddle too long. The upside of that is that the rust can usually be removed easily with a Scotch Brite scourer.
The main trouble with stainless of any grade is that there is next to no international standard for what constitutes stainless. So every manufacturer has a slightly different steel composition and therefore different properties.
Would be interesting one day to line up a selection and test their individual qualities.
TGW.