The fan theory video below is from the io9 YouTube channel. I don't think it is a particularly good fan theory but with some modification I believe the fan theory can be strengthened.
First, The final episode of Star Trek: Enterprise itself doesn't support the fan theory well. The B plot of the episode is that commander Will Riker (Jonathan Frakes) runs a holodeck program of the Enterprise NX-01's final few days before returning to Earth for decommissioning. The purpose of interacting with that holodeck program was to work through a loyalty dilemma Riker was experiencing during the Star Trek: TNG episode "The Pegasus". Riker seemed unfamiliar with the holodeck program and that using the program wasn't even his idea.
As stated near the beginning of the episode:
First officer's personal log, stardate 47457.1. With the unexpected arrival of Admiral Pressman, my old C.O., I find myself in an awkward position. Counselor Troi has suggested I might get a few insights by calling up an historic holoprogram.
That itself doesn't negate the fan theory video's premise. One might argue that the Enterprise NX-01 holodeck program became Riker's favorite after the events of "The Pegasus" and that the series was played out of order by Riker.
Maybe Riker did play the series out of order but most viewers have seen the series in order. Riker was never seen in any other previous episode.
At the beginning of this post I stated some modification could make this fan theory stronger. What if we the viewers are part of the holodeck simulation? As holodeck characters we wouldn't be aware of our existance being holodeck characters. We'd be programmed to believe we were sentient beings watching a TV series. Will Riker was in other Star Trek: Enterprise episodes going between objective and subjective modes to interact but as holodeck program characters we would perceive Riker as other faces.
I don't think that's the real whole story though. There is a character from Star Trek:TNG that is the Star Trek: Enterprise holodeck program constantly but we never see him and it isn't Riker. His identity is hidden because he's very introverted. Riker frankly wouldn't care if the simulated viewers knew he was in a holodeck program.
Counselor Troi (Marina Sirtis) explicitly states that she had never ran the Enterprise NX-01 holodeck program before yet she was able to prompt Riker to skip ahead to specific points in the program's events. Troi would have had to gotten that knowledge from somewhere such as one of her patients. The one person canonically known to have been traeted for holo-addiction by Troi is Lieutenant Reginald Barclay. Barclay is also known to have canonically ran holodeck simulations of both the Enterprise-D and USS Voyager. It's not Riker's favorite holodeck program io9. It is Barclay's. Don't blame io9 for getting it wrong. The holo-emitter has been malfunctioning lately.