Protected Content Issue when User is logged in but not a subscriber

I'm building a simple membership site for audio stories. Basically, if you are not a subscriber, you can see all the content except links to the actual audio stories.

I've set this up using shortcodes to show the story description plus non-hyperlinked list of audio files for non-subscribers and a hyperlinked list of audio files for subscribers.

The setup works perfectly when a user is not logged in and when a subscriber is logged in.

What isn't working is when there is a user who is not a subscriber is logged in. This situation causes ALL content to be blocked (except, of course, the subscription page). This case might happen when a person starts the registration process (which creates the account) but doesn't complete payment or if they cancel a subscription.

The logged-in non-subscriber has less access to content that someone who isn't even logged in. I want this person to see the same content as a non-logged in user would see.

Is this possible?