Ok, so this is a rather important topic not only for the Dead Sea Scrolls but for academic work on antiquities more broadly.

Essentially, the controversy boils down to the fact that the only scholars who were given access to the Scrolls early on were more or less Christian/non-Jewish. Jewish scholars hardly had any access to the Scrolls despite the fact that the Scrolls obviously play a very important role in the history of Jewish cultural heritage and the evolution of Jewish religious thinking. Early publications of the scrolls endeavored to show how they contributed to the history and rise of Christianity; however, as Lawrence Schiffman points out, they're equally if not more important for the history of Judaism (Schiffman wrote an entire book about the controvery entitled Reclaiming the Dead Sea Scrolls that goes through the entire issue in fine detail: https://en.wikipedia.org/wiki/Reclaiming_the_Dead_Sea_Scrolls.)

Early on, the Scrolls first publication team was indeed international (foremost among the members was Frank Moore Cross, who essentially became the father of DSS studies). Cross was given early access to almost the entire cache of manuscripts in the Fifties, in part because of his teacher at Johns Hopkins, W. F. Albright. The most important of the early finds, such as the Great Isaiah Scroll, were kept by monasteries and other places such as the offices of the American School for Oriental Research. But, as the article you linked points out, access was limited. Over the course of his career, Cross had tons of students work on various scrolls for the doctoral work at Harvard. Note, too, the vital series Discoveries in the Judaean Desert, which is the series where the critical editions of the scrolls have been published.

EDIT: I would say that the scrolls are WAY more than a modern day footnote. The scrolls have opened up to biblicists a treasure trove of textual data that has allowed us to do a much better job at reconstructing the textual history and transmission of biblical texts. Sure, they haven't necessarily affected modern religious though, but they are part of the history that gave rise to modern religious thought. As such, their controversial history of publication and treatment in academic literature has generally been a disservice to the field at least in so far as it slowed their publication significantly, hindered our ability to reconstruct the history of both Judaism and Christianity, etc.