It's noisy data. In the plots in TFA, you'll see that the residuals are expressed in meters per second. Meters! It's at the limit of detection even for our best spectrographs.
It's very hard to work with noisy data. If you work on bad data the results get extremely dependent on methods of analysis. How do you prepare the data? Do you reject outlying measurements before you even get to analysis? If so, how? Why reject *this* point, but leave *that* one? Are you doing any filtering of the data (and how)? Any windowing? Smoothing? There's a lot of tricks you can use to make bad data appear acceptable. But in the end, it's garbage in, garbage out. That other signal can very well be an artifact. Or could be real, but not a planet. Or indeed a planet. We have no way of knowing without getting more observations of better quality (which is difficult and costs a lot of $$$).
On the other hand, if the data is good, then any data analysis method will give you consistent results (provided that the method is used correctly).