Neither party has any means of holding a primary, either in a state or nationally.
Primaries (or caucuses)are scheduled by the state. They set the date. They are exclusively state-run. The state has rights under the Constitution- political parties do not.
Under this system, it seems to me that legally the parties (they are not government bodies) cannot enforce their decision. The national committees decided that primaries before Feb. 5 would be invalid, unless already scheduled and sanctioned by tradition- like NH. MI et al. The states are free to set the dates, which involve state machinery. The National parties cannot enforce their executive decisions at their National Convention without a vote.
Not only that, the parties, in the case of the Republicans, accepted a lesser number of 'delegates' while the Democrats scrubbed them all. This is discrimination, whether by government, institution or individual, and is subject to federal law.

McGrath, simple it ain't. I don't know how the parties are governed in the UK. Perhaps the systems there are more straight-forward. I know it couldn't be as convoluted as the American.