No. There are institutional subscriptions that you can lobby your university for, you can use Zotero with webDAV servers which you can find with significantly higher free storage limits (not for group storage, though), and you can of course always use Zotero and sync metadata for free.
I'd assume one major reason Zotero doesn't want to do any discounts (students, poorer countries, etc.) is that verification creates a bunch of additional work.
Upgrade Storage
I'd assume one major reason Zotero doesn't want to do any discounts (students, poorer countries, etc.) is that verification creates a bunch of additional work.