In this case, however, a pop-up on your own site costs nothing. In fact, removing it incurs costs in development time, even if it's a simple line delete.
So, I am 100% sure no marketer would ever push for removing it, unless end-users specifically tell them that they are not going to use the site because of the pop-up. The likelihood that they realize that on their own is next to zero because of the difficulties in retention analysis to catch this.
I'd say if their click through rate to the actual article (aka bouncing off the page instead of clicking the close button and continuing to read the article) is low, they'd likely remove it. At least that's how I've been able to convince certain marketers about the inefficacy of their tactics. But other things, like modals to subscribe to the newsletter that pop up after reading the content half-way, simply work too well to ever give up.
Now, that is a different take. You have been able to convince them. It's not like they realized this themselves, or that they deduced something from the numbers.
Again, only my experience at past employers, but in a lot of cases the developers don't get heard when making these suggestions.
At what point is the faulty generalization simply...a true generalization? Just because you don't want to believe it's true doesn't mean it's not true.