Pages in the "customer" folder in your theme are restricted to logged-in customers, but it doesn't require the customer have any active subscriptions. (In fact, it's where a customer with inactive subscriptions would go to reactivate.)
If you want to make a custom page (or section within a page) that requires that the customer have an active subscription, you have to loop through their subscriptions and check for any with the status of 2 (active):
{% if customer %}
{% if customer.subscriptions|selectattr('status', 'equalto', 2)|list|length %}
[Content for active subscribers goes here]
{% else %}
You must be have active subscriptions to view this page.
{% endif %}
{% else %}
You must be logged in to view this page.
{% endif %}