For the students who are becoming confused, this is unlikely to be examined, but understand the difference between what you already knew (that concentration, not amount or volume, affects rates), and what is being asked.
The only reason why volume matters is because it is affecting the way that concentration changes (which consequently affects the rate). It is through what you already knew, which is why this works. You might ask: why does the concentration change differently? How come I never thought about this before?
It's because we usually work with homogenous systems, like all-aqueous species, or all-gaseous species. This effect won't happen to those sorts of systems.
However, since this is a system where HCl is in excess and contact with a somewhat constant surface area of metal, the rate at which the amount of HCl decreases is constant. This means that if there is more volume, the concentration decreases more slowly - hence changing the relative rates as the reaction proceeds.
In a homogenous system, all particles are free to bump into other particles, so an increase in concentration also increases the amount of collisions per unit time, and so this effect (of "changing the relative rates as the reaction proceeds") shouldn't happen - I think.