How will blocking the download of a file that students already posess on their local PC help stop plagiarism? Do you have any evidence that students are actually doing this or is this yet another example of a tutor expressing a 'concern' about a new (to them) workflow?
If the concern is the original student is sharing their password so that the second student can download their submission - then as previously said, the first student has the original file anyway, so that isn't going to help stop plagiarism. On the other hand if the concern is that students are accessing each other's accounts and have each other's user names and passwords then that is a systems and security issue that needs adressing on a much wider scale than just assignment downloads!
by Richard Oelmann.