That New Scientist article does a reasonable job in summarizing the pros and cons of the three basic analytical methods LIGO and later LIGO_Virgo used. An obvious issue with template method is that the overwhelming bulk of such templates, maybe all that were used, presuppose GR is correct. The real bone of contention is the claim by Jackson et al that certain folks at LIGO and LIGO_Virgo consortium have failed to share all relevant GW data with outside researchers, and been sloppy with their own analysis of presumably full data sets. Maybe even worse - massaging some results, especially re first detection, in a way friendly to confirming GR. Don't take my summary as gospel - read the article through and form your own judgement.