Why not have the invitation be going to inbox.google.com? It's already gated behind a different URL; why force additional hoops? To weed out people who would put in the effort to go to the URL but not send an email?
Inbox probably requires Google to index your emails in a different way, for storing extra metadata for snooze returns, tags etc. Hence, there is probably a processing/migration step for would be beta users before they can start using inbox. Hence, just using a different website wouldn't have worked.
