I was able to import the shared history. Perhaps the students do not know where to look/find the history?
Have them use "Histories Shared with Me". The history will appear in their list. Then they click on the history name and use "Copy" to move the copy into a history in their account. From there, they have own copy and can manipulate/download datasets (I was able to from the test copy I made).
Hopefully this helps resolve the problems! Jen, Galaxy team