Known Limit
After review by the development team, it has been determined that this issue is related to a known limitation with the software that lies outside of Esri's control. The issue's Additional Information section may contain further explanation.
Additional Information
No Public Explanation
Workaround
1. Reproject your line shapefile to the desired coordinate system.2. Convert the line vertices to points.3. Calculate the Z values of the points using the field calculator.4. Create a new field and calculate these z values to meters in this new field.5. Create a TIN from this point data using 3D Analyst dropdown > Create/Modify TIN > Create TIN from Features > choose the point shapefile > specify the field that you calculated the z values for in meters.6. A TIN is created. 7. 3D Analyst dropdown > Convert > Features to 3D > specify the polyline shapefile for the input > use the TIN surface for the 'source of heights'. The values should be exact.