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Yes, but Spectre is an intra-process leak, so the scope is somewhat restricted.
Meltdown is a inter-process leak (and even memory-wide leak, so inter-VM). So a non-admin process on a machine could get access to the memory of admin processes on the same machine or another VM on the same host.
(Caveat: still digesting the info about all of this. Luckily it doesn't affect my work specifically.)
I thought Spectre was the hardest to solve?