Is Transdem or DEM in general inaccurate for ground distance?
The mathematical formulas in TransDEM fall in two categories: exact ones and approximations. Map projections, for instance, are always exact, while geodetic datum transformations are an approximation. TransDEM uses the 7 parameter Helmert transformation there which is as accurate as you can get with a general purpose solution. Then there is distortion, of course, since our planet is not flat, but the resulting terrain coordinate system is. TransDEM employs UTM here, which is a cylindrical projection and as long as you stay in the native zone you should be more than fine. Even if you map the adjacent zone into the current one and move to the far end, distortion should still be hard to detect.
Internally, TransDEM rounds down floating point computations to 1 mm accuracy and, by default, displays coordinates with 1 m accuracy on the user interface.
The rest is up to geo the data sources and possibly to their pre-processing outside TransDEM. So, when you use a 25m DEM, your accuracy is around 25m (a bit less than that, for the math purists). One can make big mistakes, though, particularly when georeferencing manually. However, as long as you work with pre-georeferenced stuff you should be rather safe.
In the old days, when people used MicroDEM and HOG, you could easily miss the DEM projection, which is often Plate Carrée (actually a pseudo-projection) and would end up with a huge distortion of 25% or even 33% further up north, which is a bit like watching a 4:3 TV program stretched to a 16:9 screen.
A good indicator for ground distances are UTM grid coordinates. They are in meters (as with almost every other map coordinate system, including national coordinate systems in countries which stick to imperial units elsewhere). By default, TransDEM will transfer the 1000m grid lines to the ground textures painting them in purple. Check these grid lines, compare with the Trainz 10 m ground raster and with the Trainz 720 m baseboard raster. Then check with a different geo data source, like Google Earth. Display the UTM grid there and compare with the TransDEM values. They should match. TransDEM would not work if they didn't.