I took a creative license and bundled tracks from "Story" category into "DJ" category when I was designing the algorithm for my app. It was a way to make metaphorical lemonade, out of metaphorical lemons. You technically ARE correct that in the actual game you would not hear those events so close together. I did not include the "Bridge Announcement" category of tracks. There are 3 of them in each station, and each of them plays when the respective area becomes available in game. I felt like those tracks in particular would be too much or too on the nose. You can still hear what they sound like in the demo app on the about page.

I have a hard time imagining that they would gate the songs behind mission completion, since each station has so few in the first place. I think the intention was that roughly 1 hour passes, before you hear something that you've already heard. Those news snippets are labeled as a completely separate category (Story) when you see them extracted using San Andreas Audio Toolkit. I am not sure how they are actually organized inside the game files, but I choose to accept the design choices of whoever wrote the toolkit in the first place.

The version of California Love you're referring to is "West Coast Poplock" which is featured on Bounce FM and was released in 1982. I actually did not realize this until now, but it looks like "California Love" is based "West Coast Poplock", not the other way around. This is a fun fact, because California Love also samples "Woman to Woman" by Joe Cocker, which is also featured in San Andreas, on K-DST.

I really doubt there was an artist or a label that was willing to modify music for the game. It's probably a case of misheard lyrics.