It seems to me that in a study of this kind there are two aspects to reproducibility: the raw data, and the analysis performed by the software. By including both the raw data and the actual software used in the original study, you make it possible to check each part separately. Without the original software, it's difficult to say whether any differences in the processed results are due to problems with the original software, problems with the reimplementation, or differences in the input.
Having the original software for comparison also makes it easier to guarantee that the results can be reproduced with a different _style_ of implementation; otherwise, not knowing how the original software was implemented, you might end up recreating it the same way, with the same built-in flaws. If the software is included you can deliberately choose a different approach.