And the other shoe is that surely SG-1 episodes got archived in the 21st century and are, in theory, accessible to the characters on Star Trek. ^_^
Of course there's rule #37843-A, no show exists as a show inside its own universe, so episodes of Star Trek shouldn't be in the Star Fleet database, but does this rule have a transitive property that no show that references Star Trek is in the database?
Doctor Who is a little bolder about walking right up to the line about just finding out what happened before, but it's centered on time travel and has more fun with the concept. Star Trek is far more straight-laced, but I'll bet SG-1 would have few qualms about checking to see how their own episode ends via referencing another show, if they were pulling one of their comedic episodes.