'zero-overhead' for some feature is equal to 'no runtime overhead above what one would incur from coding the feature yourself.
That definition explicitly does not include the concept that 'zero-overhead' features carry no cost when not used. In fact, the entire point of Bjarne discussing what "zero-cost" means in his response to Sutter's exception proposal, is to state that for C++ (which originated the term) "zero-cost"/zero-overhead does not mean that language features do not incur cost by inclusion in the language, like with exceptions. There is a cost to code during runtime if one does not explicitly remove exceptions from the language at compile time. Stroustrup's point is that this built in runtime overhead from having an exception mechanism built into C++ does not violate the language's 'zero-cost' guarantee.
"What you don’t use, you don’t pay for. And further: What you do use, you couldn’t hand code any better."
Ideally I would like to use exceptions as well, since they make the code look a lot neater and clearer, but I cannot justify their use in all places because of these non-zero costs.
The time to run exceptions is a lot less than to run failure checks, except in extreme cases as in the synthetic (not to say phony) benchmark presented. If the time spent throwing matters, you're Doing It Wrong.
The branch prediction slots that failure checks burn are rare and precious: much bigger than a general purpose register, and much faster than L1 cache. Blowing your branch prediction cache has costs hard to measure, although the perf registers help some.
The only substantial cost is object-code file size, and that mainly because precious little effort has been spent to minimize it, because really hardly anybody (i.e., only embedded) cares.
The problem with proving something like this is you have to build and maintain two separate sets of code for the same project, one that uses exceptions in the correct manner, and another which does error checking to the same degree. Nobody has time to do that for a significant project.