It doesn't matter if it's a CD, a Film, or manual with the instructions to build a spaceship. If you copy it, the original owner doesn't lose anything. If you don't copy it, the only one missing something (the experience) is YOU.
Enjoy!
Of course, if you happen to have some extra money for donations to creators, please do so. If you don't have that, try contributing with a review somewhere or recommending the content, spread the word. Piracy was shown to drive businesses in several occasions by independent and biased corps (trying to show the opposite).
They still have the right to distribute it. It's not like reddit, who not only claim the right but also apparently claim ownership of any content you publish there, while providing no consideration (payment) in return.
However, as you say, they have the right to deny you, and by copying you are subverting their rights. That's still not theft, though, which is why copyright infringement is a separate offense.
Theft is a crime, copyright infringement is a civil matter.
That's not entirely true.
The payment is hosting your content for free on their servers that provide reasonable uptime and unlimited retention. You can choose to carve out your own place on the internet and post your content on your own hosting if you want, but a lot of people choose Reddit, or Facebook, or Instagram, or Snapchat, because the tradeoff is agreeable.
A lot of people choose those sites because they don't understand the trade off, because the site is presented as "free of charge" while the exchange of your data is a secondary transaction hidden in the fine print of the terms and conditions. It is NOT and exchange of data for access to the service, not at the point of sale, not the way they present it.
There is also a nuance in that you have to grant them rights to your work in order for them to legitimately host the material. This is essential, but they use it as an opportunity to claim far more rights than are necessary, without any fair exchange.