metis is a first-order automated theorem prover. the metis tactic will handle encoding the goal as a first-order problem, using ~just the rules you provide it, invoking actual-metis, and reconstructing a proof (in the kernel logic) from the output proof. so, it is impossible to prove things that are false using the metis tactic (ie, metis is entirely out of the TCB).

re: the simplifier, I feel like it's a bad example because coming up with good simp rules and knowing when to add them and when not to when writing new code in Isabelle/HOL is almost an art.