CincyTrains,
It would be my guess that Amtrak is indeed running down to Mott Haven Junction on the Metro North tracks. Then returning north on Metro North's New Haven division to reach the interlock at New Rochelle. That's the only detour that I can think of, that comes close to 27 miles.
Based upon my knowledge of those tracks, it would indeed have to involve one backup move. The real question is where are the making that backup move. At Mott Haven it is possible to transition from the Metro North Hudson line to the combined New Haven/Harlem line, via a short curved track that constitutes the top of the wye at Mott Haven. There is no such wye connection at Shell interlocking in New Rochelle.
So the question is, do you tie up Metro North's very busy combined main line right before the East River bridge by stopping to reverse directions? Or do you run backwards on the Oak Point line all the way to either Sunnyside Yard or Penn? I'm guessing that they are running backwards on the Metro North line, as it's the shorter distance.
Now had they listed a shorter distance on the detour, then I would have figured that they were using a newly built freight line that runs around the bottom of the Bronx. This line, which opened maybe two years ago, branches off Metro North's Hudson line just before Yankee Stadium. It then runs on a concrete roadbed/low-level bridge, about two feet off of the shoreline, out over the East River.
This line then curves back onto land at the southern tip of the Bronx, and head back to the north into Port Morris yards. The problem here is that, as far as I know, you are still left with a backup move onto the Hell Gate Bridge from the Port Morris yards.