And in practice, on the web you're baking SCTs into the certificates (technically sophisticated customers might buy certificates with no SCTs because they know what they're doing, but that's a speciality product, lotta people buy gasoline every day, but not too many need barrels of crude oil, if you claim 2 million distinct customers served daily but then say they're all buying crude oil I just don't believe you).
To get working SCTs the (pre-)certificate needs to be logged at one of a few dozen trusted Certificate Transparency logs. Which means there's a public record of every such certificate, who issued it and when it was logged.
While this is indeed not a court and doesn't have "Discovery" the CA agreements do require the CA to provide Mozilla and other vendors with complete records of certificates they're interested in, these days that is often provided in the form of crt.sh links because hey, the (pre-)certificates† were in the logs anyway, but it's compliant to provide the data as ZIP files or whatever -- if there is such data and you have it.
So, no, independent researchers can get a pretty good idea by just inspecting a public log view, and the browsers can insist on getting the exact answer if they want it, unless of course TrustCor doesn't care about being distrusted.
† You aren't required to log the certificate as well as a pre-certificate but in many cases CAs do that too. Modern rules are clear that the existence of the (non-working) pre-certificate is assumed to imply the existence of the corresponding certificate even if you claim the certificate was never actually issued.