With a bare bottomed tank, you can remove a lot more of the waste from the tank. With gravel, no matter how good you are at vacumning, there is always a layer of "crud" that is left. That waste will be processed in the nitrogen cycle, just like the other, "fresher" waste you see come directly from the fish. The end result of that process is nitrate.
The less waste you have in a tank, the less will be processed into nitrate, the less nitrate you will have in the end. If having a bare bottom allows you to have less waste "hidden" in the tank, you will have less nitrate.
Another place where you can easily remove a large amount of the "hidden" waste is in the floss part of your filter cartridges. Between water changes it is easy to pound the filter cartridges clean in a few cups of fish water (I use a blast from the utility sink - well water with no chlorine is GREAT for that).