Or are they saying here that they don't know/have no record of a GRC for this person because they never ask the question or record the data because they are operating a de-facto Self ID system?
The advice appears to be that it is illegal to ask for a GRC. So it is entirely possible that they have no idea who’s got what.
I looked at this website and my first thought was that this is a specific trans support website and may be using a false Stonewall version of the law on this so I was going to check the actual law.
Then I realised that the MoJ are actually more likely to be using this version of the law than checking the reality so here it is...
For instance it might be reasonable for an organisation to disclose something to the police if you or someone else’s life is at risk. They can only disclose information that is relevant though, and your gender history or trans identity is very unlikely to be relent in most situations. It is also illegal for a service or employer to ask if you have a GRC, because they should treat everyone the same regardless of their gender history. To challenge a service or employer about confidentiality you can get legal help from a solicitor,
Are there extra protections for trans people?
Yes, but only if you have applied for a Gender Recognition Certificate (GRC). You don’t need to have been granted one to be protected though. Once you’ve applied, section 22 of the Gender Recognition Act says that it’s illegal for representatives of public bodies, services, businesses or employers to share your previous name, gender history or trans identity without your consent. The difference is that it’s a criminal law so instead of you needing to hire a lawyer, the police should deal with it for you. If a court finds someone guilty, they get a criminal record and a maximum fine of £5000.