In that case it made sense that the party could run primaries however they wanted to, just like the Elks could run their elections for officers anyway they wanted to.
However, it is now the case that primary elections are run by state and local political entities financed by taxpayer dollars.
It doesn't seem right that political parties can do whatever they want in the primaries if they are not footing the entire bill.
I think this is one of the reasons that states like California are moving to open primaries, i.e. if the parties aren't footing the bill then it's an open free-for-all as to who gets chosen.
Republicans tend to be against open primaries. If they want to keep their primaries closed, then maybe they need to fund the process entirely themselves.
Each state party’s executive committee can decide whether to have a primary, a convention, or a caucus — or a combination — to select delegates to the National Convention. In fact, in WV in 2008 there was a (one-time) party convention to select 18 of the 27 delegates, with the primary selecting only 9. It was unpopular, so not repeated by the state party. State law may refer to a primary, but not how many delegates are thereby chosen.