My take on this is that it is more the networks/ABC's fault. Cablevision, on a national scale, is much smaller than the Comcast, Verizon, and AT&T in regards to the total population that they can reach (not necessarily total subscriber base today).
However, the population and demographic that Cablevision does have 'control' over on their system in the areas they serve is 'coveted'. (Can't find the right word, i don't mean to say that other areas of the country are not important) They cover the NYC suburbia area (North NJ, LI, etc.) Essentially a lot of people in and around NYC - the media capital, and very important market.
Cablevision, knows they have this 'coveted' population so they are negotiating hard. A lot of these networks, in my opinion, probably did not have this type of push-back, and usually just dictate demands to their distributors. Cablevision is known to be a very tough negotiator and I have personal experience negotiating with them on a business level, so I can attest to that.
Personally, as a Cablevision customer, I am glad they pushed back on HGTV, FOOD, and now ABC. Trying to keep the rates in check.
ABC's counter-argument is that Cablevision ostensibly takes a free product (from ABC), then charges their customer's for it. I would say cablevision does have costs for distributing the 'free' OTA networks on their systems, however, it is debatable if the charge for basic cable is fair. However, if Cablevision suddenly said that they would reduce their basic cable charges by $1 or whatever (to deflate ABC/Disney's argument), I doubt ABC would just drop this.