just because we haven't mentioned that aspect of functionality in the discussed softwares doesn't mean it doesn't exist. To be honest, I dont think QSI restricts read-access to one user at a time. It does, however, restrict editing rights to one person within a document (i.e., 2 people can not be editing a document at the same time - however, if Person A puts the document into edit mode, saves and exits, Person B can go in afterward and continue the edit...assuming both have access rights to that document).
However, with the amount of document control software mentioned, you could perhaps contact the individual organizations to find out if they meet your needs....or contact the posters who mentioned the software.