As I was watching the Room 23 video, I was struck by the wide range of included materials. This video was made by Dharma, for what purpose exactly, it is not completely apparent. The main question it raises for me is, "Why did a video made by Dharma include the phrase 'God Loves You as He Loved Jacob'?" What on earth could the DI have known about Jacob? Furthermore, why did they include hieroglyphics in the Swan countdown timer and why were the Dharma school children learning about hieroglyphics in such detail? Here is my theory (or wild speculation): Charles Widmore used his fortune to fund the Dharmas Initiative and send them to the Isalnd.
We know that Widmore left the Island regularly during his time of leadership, apparently for significant periods of time if he had time to meet and start a relationship with Penny mother and raise Penny. So Widmore made his fortune and decided that the Island was too great a resource not to be used for his additional gain. He finds the DeGroots, who are interested in pioneering some interesting scientific work, and gives them unlimited funding as well as some privileged information that allows them to find the Island using The Lamppost. He never reveals to them what he really knows about the Island or that he has been there before, but he slips them small pieces of intelligence one way or another. Perhaps he had someone on the inside of the DI (Horace?) that he disclosed more to, giving the DI incite into Jacob, ancient Egyptian culture and ordering the barracks to be built over the tunnels. But eventually things take a turn that Widmore does not approve of and he orders the Purge. Perhaps it is realized at some point that Widmore betrayed the Island by bringing the DI there and this gives Ben the chance to banish Widmore and take over leadership.
Finally, as a follow up theory/question- assuming Widmore was responsible for the DI coming to the Island, was he acting on orders from Jacob, his Nemesis or on his own? I ask because Jacob seemed to want people to come to the Island, if only for a social experiment of sorts. His Nemesis on the other hand seemed convinced of the perpetual corruption of all people, which one could argue was proven by the eventual fighting and destruction that came from Dharma's presence. Then of course it could have been Widmore's insatiable thirst for power and wealth that led him to do it.