The the

"The" goes with "staff," not "Gazette." So, regardless of whether The Phoenix Gazette's style is to cap its The, that particular capitalized "the" was just plain wrong.

To use yet another of my reductio ad absurdum analogies (I didn't minor in philosophy for nothing), I submit the following:

If the president owed you money and you intended to collect, would you capitalize the "bill" in "I'm going to bill Clinton"?

Of course not. Same deal with that "the" -- it's an unrelated word that, coincidentally, happened to be in the same place as an identically spelled word that often is related (and capitalized).