It doesn't explain why it's shown a week later though. Why don't they just show it the day after?
The reality is that the loss of a relatively small number of people who'll watch online ahead of it's screening on TV is a small price to pay for the better viewing figures they'll get on a Saturday evening over a Sunday.
I think they're to be commended for doing this - it's what we keep saying, make it available legally and most people will use that in preference to torrents and other more questionable mechanisms.
And the worst part is, when you finally see it: you have no one to talk to! The world already discussed, spent a week fanboying out about the episode! They'll spend the week discussing yet-another new episode, while you hide trying to discuss a week-old episode without learning new spoilers.
It keeps you a week behind the world on discussion and prevents you from being able to use any fan media during an active season without having big plot points spoiled.
Even if that weren't the case, I don't know about the rest of the world but in the UK, at least since the Russell Davis reboot, Doctor Who is mass market.
Yes the people you're talking about exist, but they're not the majority, they're not even that big a minority (though they're very vocal). A network is always going to go where the money is and that's with the largest number of people.
Thus, Australians have to endure an entire week of UK/US discussion before they can see an episode.
I imagine many fans will continue to pirate.
Why will Australian fans continue to pirate now that the show will be available legitimately on ABC's website 50 minutes after UK transmission?
Yes, watching it on a PC/tablet/phone is not the same as watching it on a TV, but pirated versions suffer from this as well.
A Christmas Carol was same day as was all of series 6. Indeed, the need to go online for new Who has decreased. (Although I would buy the season sets when they became available to pay my dues to ensure more were made).
Back during classic Who, a few PBS stations aired some late season 1980s stuff before the BBC due to special agreements.