Given it was your first game, you absolutely did the right thing by following the distro’s advice and sending it back.
The remedies they are offering sound perfectly reasonable to me. Them opening, inspecting, and reboxing the game should enhance your peace of mind, not be a source of stress that you have paid full price for an “open box” item; in this case your “open box” pin is actually BETTER than a factory-sealed unit because it has received an extra layer of QC. Someone above pointed out that pinball is unlike any other “consumer” purchase, and this is a good example; avoid conflating an “open box” pinball machine with an “open box” laptop at Best Buy!
Someone with more experience might inspect more closely for damage and keep the game if none is found, but there’s always the slight risk that the impact which damaged the box could have also caused concealed damage somewhere in the game. No shame in erring on the side of caution, especially when the seller is encouraging this approach.