It is no surprise that Ms. Wasseman-Schultz was against Bernie Sanders. Ms. Clinton is the DNC’s flagship product, and Wasserman-Schultz was defending the brand. True: the DNC’s own rules say staff must be impartial*, but that rule makes as much sense as a Apple promising to be impartial between iOS and Android.
If Apple did make that promise, and reneged on it, then it could be rightly sued, of course.
You have correctly identified the parties as corporations. In other words, the parties themselves are special interests with their own corporate agendas, much like Apple and Nike have their own agendas.
Taking the analogy further, Nike and Apple have an entirely different agenda than consumers of sneakers and phones. Their agenda is for stakeholders in those companies to profit off of those consumers, by designing and aggressively marketing them products, even if those products are the result of an immoral system that exploits borderline slave labor in countries like Indonesia and China.
In this same way, the interests of the DNC and GOP are not the same as that of the voters to whom they are peddling their marketing propaganda. Stakeholders in the DNC and GOP gain power and wealth by leveraging these corporations, collecting payment from the voters in the form of their votes so that they can, in turn, sell influence to oligarchs, by way of their positions, to turn a monetary profit. There is no mystery why the average Senator in America in 2014 has a net worth of about $10,000,000 despite only having a salary of $174,000. They are stakeholders in a very lucrative enterprise.
So, yes, you are right that the political parties should be rigged; they are corporations, after all, and, generally speaking, corporations want to accumulate wealth. It doesn’t mean that’s what’s best for America, just best for the oligarchy that has total control of the major parties. If you agree that limiting the influence of special interests in Washington is of some merit, then it starts with heavy regulations on the DNC and GOP. Of course, getting elected officials in the DNC and GOP who are profiting off of this system to do that is unlikely.