No, the problem is that publishers take research that they didn't pay for, ask researchers who they aren't paying either to review it and then and put it behind paywalls.
Of course, researchers don't have their work "taken" by publishers; there are big incentives (via the citation count metric of academia) to provide their work to these publishers. This problem has been hashed out so many times, and I'm so upset that we're still at the status quo (especially since I'm at the end of my graduate student years, and will soon no longer have access to the university's library!)