If this is true, 3D exports use vertex color instead of texture mapping. Currently only the PLY export respects this setting. Texture mapping usually gives superior results, particularly if the texture contains fine detail or sharp edges. However if you're exporting to a 3D software that doesn't support texture mapping, vertex color may be a useful alternative.
The color at each vertex is computed by linearly interpolating the colors of the texture's nearest pixels. This works well for soft color gradations, but for sharp edges, it tends to produce artifacts such as stairstepping. Increasing the number of facets in the model (by increasing rings and sides) may lessen the artifacts, but at the cost of increased file size.