Cold air falls but that does not make the bottom the coldest part. The coldest point is on the back wall just below the evaporator or cold air inlet. The air is cooled there and starts falling.
As it falls the cold air absorbs heat from the food and the walls of the fridge continuing across the shelves and then up the front of the cabinet returning to be cooled at the evaporator. The layout and nature of the shelves affects the flow.
I'd say it depends on the design of the fridge. On one occasion I set the thermostat a mite too low on my larder fridge and some of the veg at the back of the bottom shelf froze. Yet the stuff in the veg drawers under that shelf didn't.
The vege compartment is separated from the direct airflow. It stops so much cold air getting to it and also stops it drying out. The moisture in the rest of the fridge is frozen onto the evaporator.
If you check eBay item 170568864750; it's small fridge/freezer thermometer 99p +89p postage. You can easily verify where the coldest part in your fridge is, if you're interested in finding out exactly. Just don't keep opening the door to find out.