The fact that our currently popular operating systems don't enable users to trivially 'disprove' such possibilities really shows how shitty they all are
Well apart from monitoring network traffic, with Ubuntu you can examine the source code for anything that you don't trust or dive into what system calls an application makes by using "strace".
Well you can try monitoring Windows network connections, but Microsoft do seem to love obfuscating it with connections to multiple different domains that they own.
You can't even look at the Windows source code, so your question about reproducible builds seems to be moving the goalposts somewhat.
Also, is there something like "strace" on Windows?
Edit: just looked it up and Ubuntu doesn't enforce reproducible builds, although with their new "Monthly Snapshots", Canonical is moving towards reproducible build pipelines.
The necessary technical and UI/UX difference would be capability-based (https://en.wikipedia.org/wiki/Capability-based_security) microkernels like Sel4 or Genode combined with high level user interfaces that allow one to monitor and control the rights and actual resource access and usage of programs
However, it is possible to audit the Ubuntu software against the source code which is something that you cannot do with Windows. That is a technical difference even if you don't acknowledge it.
Also, Linux does make it much easier to determine your level of trust as the different components can be analysed/verified independently (although systemd is a bit of a monolith) whereas it's a lot trickier to isolate Windows components.