It is not about the training, it is about being able to substantiate your skills. Quality certification enables you to publicly substantiate your skill set
This isn't relevant to anything I wrote, but what the hell: most certs suck, so how is this true, and why should I spend $$$ to prove that I know SQL? You should be able to get an idea about someone's ability to work in an hour or two or you can't interview anyway.
you are relying on references from you current company, somewhat tricky
I don't tell my boss, I ask my coworkers, who have little incentive to lie one way or the other.
For those coders treated like mushrooms (kept in the dark and fed bullshit), with no public recognition, shifting jobs is difficult especially if you also want to shift localities, another state or country.
Not so much in my experience, although getting exposure certainly helps.