There are a few YouTube videos that turn up on a search for Amtrak "unscheduled stop", including ones at Cortlandt (a Metro-North station) and Old Saybrook (a Shore Line East stop that does get Amtrak service, but not normally train 160).
But consider that unlike a plane, a train does not have to be at a terminal to make an unscheduled stop. Anyone who has taken Amtrak long-distance will have been sidetracked (literally), or sat stopped in the middle of nowhere, sometimes for hours, to wait for a segment of rail to clear up ahead or for other trains to pass.
If Amtrak needs to discharge passengers at an unscheduled stop, it's only logical they would choose the nearest station that can handle passengers, being a landmark as well as a place with road infrastructure, necessary whether whether you're handing passengers off to a bus, the paramedics, or the police.
Amtrak actually makes a number of regular stops at commuter stations around the country, though you cannot purchase a ticket to or from there officially.
For example, on the Penn Line of the MARC commuter train serving Washington, D.C. and Baltimore, Md., Amtrak train #151, a regular Regional service on the Northeast Corridor, stops at Perryville, Aberdeen, and Edgewood to pick up monthly/weekly ticket holders. This is noted clearly on the MARC schedule but not on Amtrak's. In fact, it is impossible to buy a ticket from Perryville to Baltimore Penn from Amtrak. An agent will not book you one, and that station will not appear in your list of options on the website or a Quik-Trak kiosk.
For a third type of unscheduled stop, there is an example from a bit further down the line. Back in 2010, a MARC train missed the Odenton station, and an Acela was conscripted to pick up the stranded passengers and return them. Odenton is not only not served by the Acela, but is not normally served by Amtrak at all.