Can Austenitic stainless steels (like Marine Grade 316) be magnetic?

The answer is yes. And this is not an indication of the integrity of the product or whether it is susceptible to corrosion. According to SASSDA (Southern Africa Stainless Steel Development Association) the following is true of Austenitic stainless steels:

Yes, Austenitic stainless steels (types 304, 316 etc), are generally non-magnetic in the fully annealed condition, however, they can become slightly magnetic when “cold worked”. This is due to a stress induced transformation of the austenite crystal structure into a martensitic crystal structure. This cold working can occur from various sources: cutting, bending, forming, machining.

Additionally, all austenitic stainless steels have a relatively small percentage of ferrite (a magnetic crystal structure) intentionally introduced into the austenitic structure (typically 3-5%) to aid in the hot workability of the steel. This will also result in a very slight “pull” on a magnet.

All of these will result in some small level of magnetic pull, and are not necessarily indicative of the product not being stainless steel, or Austenitic, or of the product being inherently inferior.