You are of course right about 1 of the 3 methods of finding planets around distant stars but I feel droithomme was more commenting on the total disconnect between the post title and the actual discovery which is nothing like 'earth-like planet discovered around a star 12 light years away'.
Thanks, yes that's correct. The key detail from the quote pull was "suggest", I didn't intend to indicate that this general method is detection is invalid.
The details in the article came down to they were pulling signal out from deep within noise in a way that other planet finders were skeptical of: "They're really digging deep into the noise here. The community is going to find it hard to accept planet discoveries from signals so deeply embedded in noise."
Even the researchers themselves are quoted as saying they don't consider anything here proven, they are just seeing if anyone else wants to have a go at finding further confirmation or disproof: "We felt that the best thing to do was to put the result out there and see if somebody can either independently confirm it or shoot it down."
The researchers themselves have not made the claim of finding an earth like planet around Tau Ceti at all. It's not been established or accepted by experts in the field that there are planets around this sun, what their orbits are, their composition, or that they are "earth-like" in a way that any non-specialist reader would interpret "earth-like". Even the authors don't make those claims. Maybe someday those things will be confirmed or disproved. Today is not that day.
The journalist is aware of this too. At the end of the article he says "If the planets exist...", acknowledging it is not established at all, before then engaging in fanciful speculation that is unlikely to appear in a reputable science news source with a competent editor: "That may just explain why no one from Tau Ceti has ever contacted beings as primitive as us."
Unless the planets happen to orbit very stable stars in the plane that sometimes puts them between earth and their star. With Kepler and some earth-bound telescopes you can discern the brightness dips from these and sometimes glean minimal spectroscopic information on the planet. Direct imaging is possible with interferometric methods and some more innovative approaches  but require funding.
The scientists took a lot of measurements over a long period, and carefully tried to remove as much noise as possible. After this, they think the remaining perturbation can be explained by a system of smallish planets. One of those planets looks like it could support life in a similar way to how Earth supports life.
There is a chance this perturbation is just noise, but the authors obviously think that the planetary system hypothesis is strong enough to ask the community for collaborating or contradictory data.
The title could have hedged its bets by adding 'might be' or similar terminology, but I honestly don't think that adds much to the conversation.
I was going to include the famous "title ending in '?'" rule of thumb, but missed the fact that the actual article and the title here differ. The actual title is of course "Another Earth Just 12 Light-Years Away?" which makes much more sense given the content.
You see, this is the benefit you get from not having experienced the 70's, everyone knows that the Grey Aliens come from Tau Ceti. Sheesh.
Fortunately, I think the last bit of annoying 70's alien phenomena will be past on December 22nd. Then we can all put to rest any question there might have been that we were visited by ancient astronauts.
Considering that is not even reaching Earth's (surface) escape velocity, the duration should not be a problem.
The pioneer probes are doing about twice that now,
the Helios probes come closer to 9x that at their closest approaches to the sun.