a very quick google of all of the information CA has on the internet shows that the intransparency of the CA system is extremely overstated in this article to put it generously

if you google "independent voter California" then you come straight to a page which explains immediately at the top that independents must request a crossover ballot to vote in the presidential primary

NPP voters, unless they choose otherwise (see below), will receive a “non-partisan” ballot that does not include presidential candidates. A nonpartisan ballot contains only the names of candidates for voter-nominated offices and local nonpartisan offices and measures.

http://www.sos.ca.gov/elections/political-parties/no-party-preference/

Let me throw in another complication. Nearly half of Californians vote by mail, ballots sent to your home automatically. Most NPP voters don’t realize that, to vote in the Democratic primary today, they must bring in their NPP ballot with the envelope, and say these magic words: “I want to surrender my ballot in return for a Democratic ‘crossover’ ballot.”

this is just a lie, go look at the California vote-by-mail application form and we see #7, in big letters:

Yes, I want to request a political party ballot for the Presidential Primary Election. I have declined to disclose a preference for a qualified political party. However, for this primary election only, I request a vote-by-mail ballot for the ________________________________________ Party.*

The only thing that sounds quite damning is the testimony of that one guy but all of the publicly-accessible information gives one the impression that CA is perfectly forthright and transparent on what independent voters have to do to be allowed to vote in the primary.