My understanding is only the high end R5 and R6 fake SINs are actually created false identities.
I'm actually pretty sure, nearly no fake SIN is created from scratch. They are mostly sold or stolen from living people or belong to dead people who "accidently" weren't marked as such. The rating is the difference in "fine tuning" this ID, ranging from something fresh and unedited, only very roughly matching your description (R1), to masterfully crafted ones that were maintained for years for a "real" digital footprint and got edited to exactly match your biometrics (R6).
Pages 363-364 discuss the nature and rules for Fake SINs.
It's pretty clear that while sometimes a low rating fake SIN is simply a stolen identity, a lot of the time fake SINs are deliberate creations. Like the famous SIN that has chicken DNA just to have
something there in case the verification system only wants to be sure there is some DNA at all on file.
The way it reads is that actually the higher end SINs are indeed invented with real biometrics, it's just not your character's.
Biometric data associated with
a high-Rating SIN will be from a real person with the
same sex and nationality as the purchaser with (if the
extra fee is paid) matching organic samples available
(blood, skin cells, hair—just don’t ask where they came
from).
As I said upthread: Think of using a high rating Fake SIN as being like the movie GATTACA.
Creating Fake SINs is something that takes a long time (page 364 says it takes years to create a high rating Fake SIN) and unless you're REALLY patient, when you buy a fake SIN you're not commissioning something to match your data. You're buying the work and artistry put in over a very long time by someone who's skills command very high prices. Odds are pretty slim that years ago when the SIN forger began work on the fake SIN you ultimately bought that your DNA/biometrics is what was used