Personally, the whole Time article had a disjointed feel to me. It makes me think (hope?) that large bits of the piece were left "on the cutting room floor" so to speak.
The version of the history of "fantasy" that the article's writer paints is utter bollocks, and I assume Terry decided that needed to be said. I didn't see it as a swipe at Ms Rowling, though, but as a swipe against lazy journalists -- but "Pratchett Anger At Shoddy Journalism" is a much less exciting headline than the one the BBC came up with.
As the parent of a new member of the Fourth Estate I know that the reporter/journalist is often very surprised when their story appears in print. They are told how long the piece should be only to have their story cut to fit the space. Their editor can also decide what perspective needs to be represented so sometimes the reporter is under orders to craft their words with a certain... um..."point of view." As Gaiman points out, the person writing the headline can also pitch the story in another direction.
The reporter is seemingly very ignorant but I am betting the editors at Time made a hash of it too.