Looks like there is some confusion here. The "Payment Methods" section under My Account page relates to saved payment methods of a customer in general and not any particular active subscription. The customers can add any number of cards on this section and then choose any of them at the checkout page to quicken the order process, it can also be turned off via the "Saved Cards" option in the plugin settings and can work regardless of whether you have subscriptions or not.
To update payment method of an active subscription, the customer will need to click on the "Subscriptions" section under My Account page and the click to open an active subscription and then click on the "Change Payment" button whereupon they can add a new card or choose an existing card if any that was previously added at the checkout or via the aforementioned "Payment Methods" section. A subscription can only have one active payment method that may or may not have been saved in the "Payment Methods" section.
I can see why it is easy to be mistaken here, but that's how WooCommerce and it's subscriptions add-on work currently. I hope you can explain this to your customers who need to update their cards.