what permission did you give the users when you created the share.  Here is what I see when I have shared an interface with someone as Editor.

If you users have creator level access on your workspace, the base inherits those permissions.

Is the Interface in a workspace that's on a paid plan?

On a paid plan, this is what it looks like when sharing an Interface:

And this is how it looks on a free plan:

Sharing an interface without giving access to a base is a paid feature I'm afraid

This is not the issue at all. The thing is, I need to have different users SEE only records that are linked to them. FOr example: Realestate agents should never see properties which are not theirs. For that, I applued user fields and populated them with the relevant agents. Then, in Interface, I use Curretn user filters that.check the user fields in the Base data.

So I must invite the collaborators to the Base data 😞

Is there another way to implement permission and privacy without populating the users in the user fields in t the Base data?

here is how I filter in the Interface:

For what it's worth, I just did this:
1. Created an interface
2. Invited another user to it with read-only access to the Interface, without giving them access to the base

And I was able to add them to a "User" field even though they didn't have access to the base, and so your workflow should work fine, really