The article says that "it will become an independent nonprofit corporation", and as OpenAI's failed attempt showed, converting a non-profit to a for-profit organization is either really hard or impossible.
> Could they not have made it into some legal structure that puts universities at the top?
As a corporation (even a non-profit one), it will have a board of directors. I have no idea what their charter will look like, but I would be surprised if at least one seat wasn't reserved for a university representative, and more than that seems quite likely as well.
So if OpenAI with billions of dollars only partially succeeded at converting to a for-profit business, then that suggests that organizations with fewer resources (like arXiv) have much worse odds.