Clarity on Cancellations Please

I've been having a bunch of issues with this plugin, but a lot of that is having to get my head around what this plugin can and can't do, however one big outstanding issue I have is cancellations.

In a recent support thread I posted here I was given the impression that for a subscription using PayPal Express with recurring payments, cancelling a subscription on the website would not cancel the subscription.

I just want to make sure this is the case, because if it is, that is utter madness. If this is a limitation of a PayPal API or something, there shouldn't even be a way for people to think they've cancelled and still be charged.

Can someone please clarify how this works for me? Is there a payment gateway I can use for recurring payments that allows people to cancel their subscription on the website that also cancels payments?

I do not feel comfortable setting up a site with a subscription where it is so easy for a customer to be charged unwillingly. I hope I've just misunderstood.