This theory is entrenched in the idea that the incident (Season 5 finale) caused a fork in an otherwise linear timeline. Therefore, all the events that happened up until Juliet caused jughead to explode still occured.
For starters, the two timelines must be related. The writers have been very good at subtle reveals which keeps us guessing, but episode 6.07 offered the biggest hint yet.
Ben's father tells him that he wished they never left the island because Ben's life would've been different and he could've been so much more than a history teacher. This leads me to believe that "Sideways" Ben and Roger were a part of the DHARMA Initiative that Sawyer, Miles, Juliet, and Daniel joined. This also means that Dr. Linus would have been shot by Sayid, healed at the temple, and returned to his father. I imagine the events at the end of season 5 enabled Roger to understand how important Ben is to him, and because of the dangers they experienced, Roger and Ben probably caught the next sub off the island. Sometime after they left, other events were set into motion causing the sinking of the island. I blame Radzinsky...
So young Ben, who befriends Sayid and helps him escape, would certainly remember the face of the man who betrayed his trust and attempted to murder him. In the sideways timeline, Dr. Linus will eventually encounter Sayid, and a very intense sequence of events will play out. Ben will be frightened by this "ghost" from his past, but Sayid will have no recollection of having shot Ben.
So what exactly is the Sideways timeline? Course correction. The events of the original timeline were always supposed to happen. Ever since the incident, the universe has been subtley trying to get back on track, which is why our characters are intermingling in the sideways timeline. They will continue to cross paths and establish relationships similar to the island timeline. Eventually, we're going to see the deaths of Dr. Arzt, Boone, Shannon, Charlie, etc. The "candidates" will continue to realize that things aren't exactly 'right' and gain the faith they need to understand their ultimate destinies.
Thanks for reading...