To summarize Verizon's statement: paying Verizon customers are demanding lots of data from Cogent (i.e. streaming lots of Netflix movies). This is requiring Cogent to pump a large volume of traffic to Verizon's network because paying Verizon customers are requesting it.
In turn Verizon is now demanding more cash from Cogent because Verizon paying customers are requesting that traffic. The end result is Verizon looking to make more cash off of their own customers' activities and/or using it as an excuse to quietly degrade the Netflix experience (but hey, they conveinently have their own Redbox Instant streaming service that I'm sure they would love you to subscribe to. It probably doesn't suffer from this problem either).
In reality, Verizon should:
1) Realize that this is on them and they are not providing the quality level of service that their customers are paying for.
2) Join Netflix's (free) Open Connect. This would both significantly reduce the congestion AND provide even higher quality Netflix service. (Hint: Your paying customers would love you if you did this, Verizon)