Here is the thing, legally, he never won. Never. His wins were stricken from the record books. When he crossed the line with the shortest accumulated time those years, everyone thought he won. SCA thought he won. Lance thought he won. Lance's attorneys thought he won. I bet both parties in the SCA case refer to the fact that Armstrong won, it is simply SCA's contention that he did so using performance enhancing drugs (which evidently was not wording included in the contract between Armstrong and SCA, which is in part what precipitated the settlement), but I feel fairly certain that there wording was that he "won" with the help, not that he never won. I am also quite sure that Armstrong's attorneys asserted that Lance won.
Here is the problem: He never won. The operation of this may seem esoteric and difficult to grasp, but at the time they settled, the reality is that Lance had in fact NOT won because he had disqualified himself at that time. Sure, the decision on that didn't happen until this month, but that should not matter. The titles should not have been awarded, and the events that precipitated that did not occur this month. Those events actually occurred PRIOR to his being awarded each year's trophy. He was doping during those Tours. Hell, he was doping every week of every month it sounds like. Because of that, at no point in that time frame did he qualify for the titles he received.
Both parties to the settlement agreement (SCA, Armstrong and his attorneys) mistakenly believed he had won. In fact, everyone did. But that does not change the fact that he hadn't won. If he had won, those wins will still be in existence. Certainly I can see that this is a pretty esoteric concept, but many times, concepts of law are really esoteric.
But as always, I am merely a student of law. I could easily be wrong, but in this instance, I would be willing to argue pretty hard and long that I am not.