Consider two processes on a *nix system, and for the sake of argument let's say they're sufficiently isolated from each other as to have only one communications channel between them. If that communications channel is a unix domain socket, one process can send a file descriptor (effectively a capability) to the other over the socket. Each process has a file descriptor table in the kernel whose integer keys are only meaningful to that process in particular, and the kernel provides a mechanism to transmit file descriptors across a socket. The kernel mediates in this case.
If the communications channel is not a unix domain socket and is instead something like a TCP connection, you don't have this option available to you.
You aren't always just sending bits from one process to another!
No, you’re using the same sleight of hand as the paper.
Boebert’s objection is about whether Alice can transmit unauthorized authority to Bob across a security boundary that’s supposed to prevent that flow. Your SCM_RIGHTS example is a case where the kernel is deliberately providing a sanctioned channel for authority transfer, with the kernel’s blessing, between two processes that the kernel does not consider to be on opposite sides of a mandatory access control boundary. Unix has no (*)-property. There is no “high” and “low” in the Bell-LaPadula sense on a standard Unix system. So of course the kernel mediates the transfer cleanly; it’s not enforcing any policy that would be violated by the transfer.
The moment you try to extend this to the actual case under dispute—Alice is “high,” Bob is “low,” and the security policy says high-to-low information flow is forbidden—then if the kernel refuses to deliver the fd across the boundary, the security property was enforced by the separate MAC layer, not the capability mechanism.
The conflation which is endemic in this whole debate is between “capabilities as a kernel-mediated authority mechanism” and “capabilities as a property that holds across all observable behavior of the system.” Unix file descriptors are the former. Boebert’s objection is about the latter.