A fundamental principle in golf is that players are responsible for calling penalties on themselves. Violating the rules and then waiting around passively for someone else to notice and call for the penalty is regarded as cheating. This is not the case in other sports (the 'Hand of God' etc.)
So I can understand that Tiger had an incorrect understanding of the rule in his mind when he made the drop, but when the issue was pointed out while he was still playing the round, he must have focused on what the real rule was. Then he must have realized that deliberately dropping two yards behind the original spot was a clear violation of the rules. That is when he should have called the penalty on himself. Instead, he silently allowed the officials to believe it was simply a matter of unintentionally being a little off in determining where he had hit from before (which is not something that can be precisely determined in any event).
He had a clear opportunity to rethink whether his drop was legal before he signed the card. By that time, knowing what the rule is and knowing that he had intentionally dropped two yards behind the original spot, he also knew that he had violated the rule and had to take the penalty before signing the card.
Conclusion: Tiger should have been disqualified. The events occurring after he signed the card were irrelevant.