I think the onus lies on the distributor (Amazon, Hulu, NinjaViedo) more so than the consumer. I do believe the consumer holds a relative degree of responsibility (and I guess this is what should be determined by a court) - e.g. it's obvious with Ninja, but some sites might not be so obvious e.g. if, like Amazon, Netflix distributed a movie that they did not have rights to -- then it falls on them.
OK, if the court can determine whether a consumer has a degree of responsibility, surely a consumer can determine if she's participating in a "copyright infringement"? If you search the Web for "watch big buck bunny online free" and download/watch one of the found files, can you tell when you infringe copyright and when not?