Nintendo's lawyers' attacks are on whichever fangames attain high popularity in the general public eye. It's possible for a fangame to become popular among a small subgroup of people without it becoming well-known to the public (Sonic Robo Blast 2 comes to mind). A general Nintendo fangaming convention should have a fairly wide profile compared to the audiences for the individual games involved.

All publicity increases risk, but different types of publicity induce different amounts of risk. No Mario's Sky was shut down because it gained a lot of publicity in the general gaming public in a short time. Pokemon Uranium was shut down for having a massive userbase. The Metroid 2 remake was shut down when it had a publicity spike at release. They all had other factors that made them slightly more dangerous in the eyes of NoA's legal department: NMS was named after an unassociated brand, PU's name was too close to the naming conventions of official titles, M2R was a remake, but a publicity spike was what ultimately did them in.