It did also spill over to all publishers. There were public burnings of comics at churches and book swapping crusades at schools and libraries. These actions did not concern themselves with publishers or content.
Harvey had quite a few horror titles in the 50's. Plus, any publisher of periodicals would see an advantage to having rack spack taken away from another publisher if only to give them potential to take it.
You are certainly right about Dell though. They didn't care about EC or any of the competition because often outsold anything else on the stands (especially if it said "Walt Disney" on the cover). They damn near bragged about it during the Senate hearings by telling Congress under oath that they sold 5 million copies of Walt Disney's Peter Pan the previous year. Of course Dell and the Classics Illustrated people both refused to belong or submit books to the Code as well and had the clout to do so.
Gaines didn't invent the idea that the other publishers stacked the Code against his titles as a conspiracy theory. It is a matter of studied, reviewed, and published history in comics.