I never said the CEO was not the top authority, I said he does not determine wages; managers do
Theoretically they could. The CEO has the authority to override or micromanage the managers. Some companies might give greater autonomy to their middle and lower level managers, and some don't. But it's hardly automatic or set in stone, as you seem to be suggesting here.
Managers run the store, and it is their job to pay employees based on what the store can afford to pay them
HR departments also seem to have some level of say on this, since they have to remain on guard against discrimination lawsuits. If a manager is setting pay rates based on their own personal biases, then that could lead to expensive lawsuits for the company.
I suspect they provided answers that were reasonable to their satisfaction, just not yours.
Actually, there was one answer which was reasonable, at least in the sense that they provided actual numbers. They showed an example of a CEO under whose leadership the company made higher profits than the previous CEO. That was at least something tangible to deal with, although they couldn't really connect the dots or prove the causation behind the correlation.