The two aren't related. You're confusing names and titles. Strictly speaking, all the publications you cite have "the" as part of the name, and it should therefore be capitalised. However, this is what it says in the Guardian style guide under the entry for "the" (lc = lower case; uc = upper case)
lc for newspapers (the Guardian), magazines (the New Statesman), pubs (the Coach and Horses), bands (the Black Eyed Peas, the Not Sensibles, the The), nicknames (the Hulk, the Red Baron), and sports grounds (the Oval).
uc for books (The Lord of the Rings), films (The Matrix), poems (The Waste Land), television shows (The West Wing), and placenames (The Hague)
The
Guardian Style Guide, though only a guide, is usually the best source to consult for questions like this.