I think you are under the impression that we offer a service like dropbox where files are synced back and forth between multiple machines. Personally I'm not a fan of these services for a great many reasons. One being the way they handle your scenario. But really, a service like dropbox only does simple file syncs. Our service can do simple file backups, but it also does more advanced and difficult backups such as database (MySQL, Oracle, MsSQL, Exchange, ect.) and full VM backups. Additionally it can run custom commands before or after a backup is scheduled. Then it emails our clients to report the success or errors during the backup. Unfortunately, because we opted to be able to do these advanced backup types, the system isn't feasibly able to function like dropbox. I hope I understood your question correctly... Let me know if not.

EDIT: Maybe your are asking what happens if multiple computers are trying to access a file when it is backed up? In this case VSS is used to backup the file side-stepping the whole open file issue. VSS isn't available in linux though, so the backup of open files fails. Usually though I found that my linux clients are usually only using MySQL backups on linux or they do some fancy footwork with the pre-command option. (we can launch a shell command and wait for it to complete before starting a backup)