While they might hold that information, what else does it have or not have?
We're told that the SIN has a lot of information, including things like job history, licences, medical and education history and the like. There's pieces of information that we don't have a concept of that the SIN would hold as a basic. Not just things like fingerprints, retinal patterns, any sort of unique biological identifier, birthmarks etc. To say that just because it contains 'name, age, nationality and sex' and that's all it transmits is a little silly.
Especially for health, if you're highly allergic, diabetic, sensory impaired, that type of information in an integrated network would be truly useful and would be 'public' to those with access, which I would suggest include law enforcement, emergency first responders. If you're going to argue that information is being withheld, you're missing perhaps the worst, most depressing points of the world.
As smart as people are, if they're suspicious, they're suspicious and on a whole will act on it. If you have such a clear pattern of what a Corp Born SIN looks like, it will get copied, more accurately attempted to get copied. If the real thing gets mistaken as a fake, say hello art world, they will get pulled in and they will get noticed. Sure, there's going to be some short term trouble for the officer in question. Sure, lawyers are going to scream murder, civil rights, discrimination and 'profiling', but there was grounds for suspicion and the officer either got permission to act on, or acted on in their own right.
The system openly discusses racism, this is in effect, a product of that world.
Short of a written charter from either Lone Star or Knight Errant, a corporate code of ethics/legal code or a national law with provisions for corporate legal extraterritoriality we're left with logic and implication. To say that a beat cop who sees what is in effect, two different licence plates on a car and does not investigate or report, is foolish. In Shadowrun's world, at least on an ideal level, it would be seen as gross incompetence, negligence and grounds for immediate dismissal. In a world of needing a job and end net worth effectively defined by that job, you would do anything to defend that job. Including what I would suggest, is raising the odd bit of trouble, if important biometric or identifying information is either missing, concealed or redacted, it warrants inspection. Verification before trust, any trust.
Especially if you really want to play the card that the SIN makes you a legal person. If they mark your status as a legal citizen, it has to be you that uses it. It has to be yours that you advertise. If anything is mismatched, it should be immediately investigated to determine your legal status. If you're at all familiar with authoritarian states, ideological fascist models of government, you'd appreciate just strict these systems can be. Add onto that fifty years of big data, analytics. You guys really don't know how bad it is.