You don't own Netflix content. You pay for temporary access to it. If you could use root access to compromise the app and pirate their content, that could cost them licensing deals and lots of money. If you can't use root, that costs them little.

You don't own your credit card either. The piece of plastic is actually owned by the bank. As they will likely be the ones that take a loss in the event of fraud from malware breaking into Android Pay, but similarly they gain nothing from letting you root your device, so their behavior makes sense.