Earlier quoted context omitted.
They test how a series of branches are predicted after returning from a hypercall, which lets them basically dump out the state of the BTB. From that, and knowledge of where the branches are in the hypervisor binary (the binaries themselves aren't really a secret, only the relocated load address is) they can figure out the load address of the hypervisor. See the section "Reading host memory from a KVM guest / Locatin…
But if you use AMD ASID it blocks this as memory mappings for VM guests are in a completely separate address space. What I was wondering was for local OS user mode to local OS root / kernel mode access; i.e. user to kernel privilege escalation.
What would block it is flushing the branch predictor state when switching privilege levels and/or address spaces.