Though Sorcerer Dedication says to choose a bloodline, it doesn't ever specifically state that your character actually obtains or possesses said bloodline. It references "your bloodline" several times, but it's unclear as to whether you actually possess it, or if it was simply shorthand meaning "your bloodline choice."
The distinction may be important for things that require having a bloodline as a prerequisite or similar rules mechanics.
"Choose your bloodline" is the language the sorcerer class itself uses.
I don't really see a reasonable way to interpret the rules in the way you're suggesting they be interpreted.
Ah, it didn't occur to me to compare it to the language of the Sorcerer class ability itself.
Good point. Thanks.