For example-
“DALLAS- Six days after being adopted in California, a so-called Amber Alert system to quickly spread word about child abductions helped save the lives of two teenagers.”
Why wouldn’t they say “the Amber Alert system”?
What causes something to lose its “so-called” status?
“So called” should be used to indicate when the name being given for something either is so unusually colloquial-sounding as to need emphasis (“the so-called strange quark”) or, more frequently, is the unofficial nickname given to it (“the so-called good cholesterol”). In the latter use, it is a short way of saying “this isn’t it’s real name, but this is what people call it.”
The term can also be used derisively as a way of highlighting the inadequacy of something to live up to its name (“the so-called improvements in WindowsXP”). Because of this, it should be noted, the term carries for many people a certain negative connotation even when used for the first purpose.
Personally, I would not use the phrase, “so-called Amber Alert System”, though I have seen such phrases used. It is used when there is a logical disconnect between the term and what it represents. I think it more aappropriate to use a phrase such as “designated the Amber Alert System by California police officials (or who/whatever coined the term).”
I prefer to use “so-called” as a challenge to the legitimacy of the term as applied to the object. Such as a defense attorney challenging the “so-called” expertise of a prosecutor’s witness.
In other words, something’s “so-called” when it isn’t, and isn’t “so-called” when it is. 
Basically, yes. Gotta love the English language 