That study does not appear to have accounted for the replacement factor as Siegel's study did. Siegel found that among women, firearm suicide increased with an increase in gun ownership rate, but non-firearm suicide decreased with an increase in gun ownership rate by a like amount, indicating that the firearm suicides among women were simply a replacement for non-firearm suicides. The same was not true for (some) men.
In particular, it appears that half of the firearm suicides they tracked in the California study were women buying a gun specifically to commit suicide. Were these women not to buy a gun, they would obviously find another method to commit suicide.
The case of California is very interesting, because their numbers diverge heavily from the rest of t he country, and you can see it in the means, methods, and procedures of general firearm ownership and use. In the south where I live, you can rent a gun at a gun range, try it out, and such, with no problems. I've heard tell that this ordinary practice is almost nonexistent in California, because of people literally renting the gun to shoot themselves on the gun line. This basically never happens here.