There are a lot of different kinds of somatosensory receptors (touch, temperature, proprioception, nociception, introception), and it's hard to tell which receptor would be most suited to transducing a magnetic stimulus, much less if it truly does. I think, to be honest, we can't really know what the heck true magnetoception is until we grow some magnetite crystals in our noses.
So magnets act as an electromagnetic energy -> kinetic energy transducer, which is what certain somatosensory receptors are good at detecting (i.e. SA-II and Pacinian receptors).
I think the issue you raise is word/term-based. Does "magnetoception" mean you have perception of magnetic field information, independent of the sensory pathway? Or does it require the use of a sensory pathway that evolution produced specifically for that type of information? Does it have to be the same type of perception of EM-fields that other animals have? I imagine magnetoception is not consistent across different animals.
Implanting magnets in your finger-tips could be considered a "hack" for translating magnetic information to a domain that allows for non-magnetic (e.g. SAII/Pacinian) receptors to fire in a manner that is tightly correlated with a surrounding EM-field. In that regard, you are successfully transmitting magnetic information to the CNS (albeit in an atypical way), and the central point of debate is: is the brain capable of decoding that as a new perception, independent of what receptor/type of receptor sent that information up the system?