A counterexample is if you build a huge non-inverted pyramid and then put an extra brick in the middle on the bottom. It wouldn't balance but you could easily imagine putting many tons of weight on that single brick sticking out on the bottom like this, thus technically causing the lowest level to mechanically fail. This is pedantic, but I think you asked for it:)
Assuming the rest of the pyramid base doesn't end up flexing around that one brick (which would not be very tall) and distributing more of its weight on the ground...
