Is there an express on the schedule that does stop there pretty close to it?
On the Main/Bergen Line, there is one peak hour local train that skips Ramsey 17, #1158. It makes all other stops from Suffern to Hoboken via the Bergen Line. Train 54 is a Port Jervis Express that runs at a similar time and does stop there, but skips all the other stops between Suffern and Secaucus. They figured no one would take the local with the express right behind it, so it skips the stop that the express stops at.
I'm guessing 3864 is a similar case to 1158 and 54.