This is a poor example.

1) Google rankings fluctuate all of the time. Every day in fact. If you look throughout this forum, or any forum, you'll see threads started virtually every day about how someone's site has dropped. You'll also see reports of they they recovered. You'll see reports of everything. Google's algorithm is constantly in flux and thus so are their results.

2) Google doesn't report all backlinks when you do a backlink search. They also only update their link: search results every three months or so. This means the information you see is stale. This means you can't correlate what you see in their link: searches with anything you see in the SERPs because not only do you not have all of the information but that information is stale. Even better, they update their rankings daily which means as soon as they find a link it would affect your rankings. So that link couldn't suddenly appear and hurt your rankings. It would have happened the moment they found it although you wouldn't have seen that link for weeks or months doing a link: search.

3) Did you take into account other factors in how sites are ranked? How do you know the sites ahead of yours didn't acquire quality links or do other things to improve their position? Maybe you had a quality link to your site removed and never knew about it? There are lots of reasons why a site moves around in the SERPs. And this search term is so uncompetitive that a site can move up in the SERPs quickly with one good link. Losing a good link can have an equal affect.

4) This wasn't a controlled experiment. Not even close actually. You literally made a declaration that link hurt your rankings based on a simple incorrect observation.

5) This still doesn't address why links would hurt a site. There is no logic to it and I haven't seen any logic given. Again, if this was true everyone could take out their competitors with poor links.