Ok, I think I have a work-around (actually two).
When you re-install the app, there’s a glitch where it doesn’t select the “Active Course” properly. To fix this, go to the “Settings” tab, and just under “Active Course” will be an empty box. Touch that box, and it will bring up a list, with Course 1 at the head. Select that, and tap Done. Now go to the Lessons tab, and try to download any lesson. It worked for me after making that settings change.
Now, you may be wanting to access Level 2 and beyond, and have discovered that it won’t let you login. Do this: when it rejects your login, it has left the keyboard still up. Hit Done to close the keyboard. Now, hit the “Login” button (again). This time, it will (hopefully) succeed (it did for me).
Update: I tried uninstalling and re-installing the app again. Just selecting Course 1 isn’t quite enough to get things working. What did work was to select something else in the list, then select Course 1 again. That worked (and matches what I did when I was testing this workaround earlier).