Look a little further down in the next paragraph of the article quoted from that post and you will see this. I am responsible for the highlighting.
The Senate accords its majority leader prime responsibility for
scheduling. He may carry out this responsibility by moving that the
Senate proceed to consider a particular matter. By precedent, he and
the minority leader are recognized preferentially, and by custom only
he (or his designee) makes motions or requests affecting when the
Senate will meet and what it will consider.
Notice that this is BY PRECEDENT only and only to prevent a chaotic amount of bills from being introduced. Any member of the Senate can introduce something to the floor. This can be prevented by objection of any member of the Senate.
This marks the third time that McConnell has blocked House-passed
government funding bills in the past two weeks. Under Senate rules,
any senator can ask for consent to vote on or pass a bill, but any
senator can object.