Bribarian and Caeruleus: WELCOME ABOARD!
Yes, it's true. The game doesn't show realistic depth changes - it's all done in generalities.
Besides asking the Navigator for Depth Beneath Keel, you can also go to his station by right-clicking on him from the Control Room. Once there you'll see a device on the wall called the Atlas-Echelot. It has a button you can click to see the depth for yourself. It is a little hard to read though.