Oh, nice idea, running Screaming Frog on a server.. I passed your notes along to our Dev team, we'll see what happens.

How exactly did you do the no-index? Robots.txt? Meta robots tag? Manual removal via Google Webmaster Console?

Beyond that, I have seen some paid traffic misattributed as organic before, which we caught because the organic landing page had campaign parameters attached specific to paid Bing campaigns.

We'd find the landing page in organic landing page reports as something like:
http://www.blablahsitewhatever.com/landingpage?s=bing|display|20150826
instead of 
http://www.blablahsitewhatever.com/landingpage

It's clearly not an organic hit since it came through a paid channel, and yet gets classified as organic. (We got around it by building a custom report for organic landing pages that specifically filters out landing pages with those extra parameters.) So from this we know it's entirely possible for traffic to be misattributed as organic when it's clearly not. But unless you can clearly see it in the URL like that, it's really hard to suss out.

Honestly, I would avoid using the same titles as a competitor. You want to stand out in the SERPs, not look like everyone else. It is possible to optimize your titles and still make them different enough to catch a searcher's eye.