"China’s courts must firmly resist the western idea of judicial independence and other ideologies which threaten the leadership of the ruling Communist Party, the country’s top judge was reported as saying by state-run Chinese News Service."

  "People’s Courts at all levels must disregard erroneous western notions, including constitutional democracy and separation of powers, Chief Justice Zhou Qiang was reported by the news agency as saying at a Supreme People’s Court meeting on Saturday."

That said, rule-of-law doesn't imply anything about the sources of law. In China a Party edict may be law just as much as legislation passed by the nominal legislative body. What rule-of-law demands is consistent and uniform application of the law, whatever the source. Judicial independence may be sufficient to achieve that, but it's not strictly necessary.

Most Western democracies don't have the strict, tripartite system of government as the U.S. Judicial independence in Europe arose organically as a de facto separation of powers, just as it did in ancient Rome. Over time leaders and governments figured out that things went more smoothly if they refrained from interfering with judicial proceedings, especially when you have a high-status judicial class that self-polices (where the social status of judges is dependent on them staying above the fray of lowly personal and merchant affairs, and that social status sufficiently substitutes for material wealth that there's little incentive for corruption). To a large extent judicial independence is more normative than anything, dependent on executive and legislative restraint and more general social expectations. Such norms could in principle take hold in China even with their single-party system.

Arguably such norms are taking hold. It's just that, like with poverty, they're starting from a very low point. Depending on how you want to spin it, either they haven't come very far or they've come tremendously far.