Starz isn't turning it's back on the internet, Starz realizes the internet is where it's financial future lies and so it wants more money from the internet. And it's betting that it can take Netflix for more then Netflix wants to pony up today.
And maybe Netflix will pay a higher price to keep that content or maybe they can get by without it (see my link to Reed Hastings' comments). But even so this pattern is going to repeat over and over with every other media deal Netflix has as internet tv mainstreams and cash rich Amazon, Apple and friends bid up the price of net based content deals.