But not by the defenders of the Earth. Not by Unit or by any government body.
Jack is a defender of the Earth, and Torchwood is a government body.
In any case, so what? With the resources available, it was possible for Earth to defeat the alien threat. In fact, it turns out defeating the alien threat was easy - it took them about a day, if even that, to figure it all out and get the necessary mechanisms in place.
Jack is clearly an unusual individual. Pointing out he's a defender of Earth and that Torchwood is basically a QUANGO of sorts is kind of playing with the semantics of the situation.
Yes, he technically is those things, but he's also not off this Earth or its technology. He brings an alien element of his own into the situation and thus is not your typical defender of the Earth or member of a government body - which, without his involvement and unique characteristics, would be unable to cope with the situation.
I would not call the events either easy nor a win.
But it does outline nicely the philosophical point of the show.
"Torchwood is the Adult 'Doctor Who'" had major problems as a concept.
At first, it was more like a teenager's Doctor Who--the only things adult about it were sex and swearing.
The remake of Battlestar Galactica. That, plus wrestling, put SyFy on my 'skip" channel list.
How about "SciFi Channel" changing to "SyFy Channel". That was pretty much a knell of doom for any future project. Yeah, let's rename our company in such a way as to show we're totally abandoning the company's fundamental market and premise.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.