Is this a legit approach?
No, not really. Google has never confirmed the use of CTR as a ranking signal for their search rankings. And, services such as these point to the fact that if Google did use CTR as a heavy ranking signal, it could easily be manipulated. That's what this service is proposing they are doing, manipulating the search results.
Now, does CTR actually impact search rankings? It's only speculation at this time and does seem like a logical factor to influence ranking. Google wants to show the most relevant results to the user; the results that answer the users search query the quickest and most complete. However, I don't think it could ever be a heavy impact ranking factor because it can be so easily manipulated.