I originally had those options used, changing the max plot points only changed how intricately the model was mangled.
ListSurfacePlot3D[
Import["C:\\Users\\Ellis\\Documents\\theheartP4.obj", "VertexData"],
PlotStyle -> Texture[ExampleData[{"ColorTexture", "CheetahFur"}]],
MaxPlotPoints -> 35, Mesh -> None, PlotRange -> All]

I have also used a few different models in case somehow the vertex data was incorrect prior to projecting a texture onto it.