Maybe because Hollywood has ALL the leverage here? Who's to say that they wouldn't pull EVERY movie/show from Netflix or demand even higher fees in response to something like that, leaving Netflix with almost no selection aside from indie productions?
I did consider that, but Hollywood seems like the last people around who would get up on their high moral horses in what is after all, an image-based battle. It would just be Netflix doing exactly what Hollywood does as a matter of course - image management plus extremely aggressive business practices. They should respect Netflix for being a savvy player instead of what they are now, a bunch of hapless clowns. The way they've blundered is a professional embarrassment, and their business partners are probably questioning their credibility as a corporation now.
The Hollywood honchos would be smart enough, and grownup enough, to understand and respect the strategy behind the campaign and not take it personally - anyone with a thin skin isn't going to survive in Hollywood anyway - and after all, it's not like anyone's going to hate Hollywood so much they stop going to Transformers movies and other twaddle. An image-based battle wouldn't really hurt Hollywood's profits at all, and as long as the profits are safe, who really cares how Netflix sells itself to its customers?
If Netflix is nervous about the reaction, they can brief their business partners in advance. Netflix is good cop, Hollywood is bad cop, the money keeps rolling in. I'm not saying that Hollywood is "really" the enemy, it's just a branding campaign to help sell the idea of charging more money that Netflix and Hollywood splits. See the difference between that and an actual feud?
And the branding campaign wouldn't be as blatant as I've made it sound. I was describing it in a blunt manner just to get the point across. That kind of language would never see the light of day beyond Netflix's internal brand strategy white papers (even those would be less blunt and more professional sounding). There are ways to make Hollywood the enemy without being obtuse about it - some of the slicker political campaigns would serve as a good model.