Ok, this is actually quite a complex question, because it deals with 2 parameters which are sometimes independant of each other. Airspace and ATC control.
Broadly, your manual mentions something about something happening when you go off the coast of the US. That is BROADLY, because it doesn't always happen.
What they intend on saying here, is that at the BROAD 12nm point the accepted standard of floor and ceilings of Class G and E are changed.
G when not depicted is at 1200ft AGL, here the boundary of your new height will be depicted (not always so clearly) by a wiggly line denoting a change in the floor of E, and ceiling of G. By the way looking at a Los Angeles sectional you would be hard pressed to find them, may I suggest you look at a Miami sectional instead (you can do so here
Now there is a reason for this change, it is primarily due to airspace control. Out in open sea, ATC releases that airspace below the new floor of E to G, meaning you can almost do whatever it is you want in there, they simply don't expect IFR traffic to fly this low, hence positive control of a flight at this height is not their problem anymore. In simple words, you are VFR or you are simply not.
Class A remains unchanged, at least to the next point, which would be sovereignty over water.
Now, as Fastyjetty mentioned, the simple fact that you are in Government Free airspace does not mean that no one is looking at you, and that you can zoom in and out all day, quite the contrary, and this is were the ADIZ nightmare starts. Familiar with it? No? Well that's the place where you have a date with ATC in accordance with 14 CFR 99 (yes, more of this title 14 stuff) within a specific time frame (15 min prior zone ingression IAC with the DVFR you filed).
That should have answered your question. Noting in the process that Airspace/ATC/Radar Control/Air defense are most times in coherence with each other, but are actually independant.
A little mind boggle for you: Did you know that you could have an active controlled tower at a class G airport??? Sounds ridiculous doesn't it! Just another example of what seems and what is.