The phrase "conspiracy thing" refers to an idea or theory that suggests a secret plan or plot by a group of people to do something harmful or misleading. Full definition
I wish the author had dealt with this issue a little more, and the whole conspiracy thing a little less though. (bookbrowse.com)
Let me just chime in here to say that I, too, didn't sense any sort of conspiracy thing going on here in an effort to get parents to buy school lunch. (thelunchtray.com)
This isn't some sort of conspiracy thing where Samsung is trying to force you to buy a new phone. (androidcentral.com)