If you've enabled user impersonation in Google, permissions will work a little differently. When any Google SSO users book rooms in your organization, Robin will always try to create the event as the user first, before falling back to the booking account. To avoid problems around rejected meetings, you should make sure they have permission in G Suite to schedule on the room.
If done successfully, you will be the organizer of any event you book via Robin apps instead of needing an invite from the booking account. Keep in mind that impromptu meetings booked from room displays will always be from the booking account for security reasons because we can't reliably determine who physically presses the button.
This guide assumes you're using resource calendars.
How to set permissions for user impersonation
The easiest way to make sure permissions are valid is to go to your admin panel in Google, then go to Apps > Calendars > Resources and check this box:
A little further down the page you should set your resource calendars to at least "Only free/busy information", but "Share all information" works too.
This setting may not apply to resources you've already created, so be sure to confirm their sharing settings match the setting above:
Once you've confirmed the settings are in place, you can enable impersonation via Manage > Integrations:
You'll now be the organizer for any new events you create through Robin. Anyone signing in without Google SSO will book via the booking user.