You are correct, the advise you received is dead wrong.
You can dump your tanks if they are not full, provided you can add water to rinse them out and push the remaining contents out.
If your camper came with an outside hose washer connection, then you can always attach a water hose and let it spray out the tank. These work pretty well, but also are prone to getting clogged up over time.
Another option is to drain the tank (even if not full), then fill it about half full by running water in the toilet, then flushing.
Another option is the drain the tank (even if not full), and back-flushing the gray water into the black (if both tanks drain at the same outlet). You attach a flush king style 3rd valve. Drain the black completely. Then close the flush king. Now open the gray and let it back-flush into the black. Wait about 10 seconds and then close the gray off again. Now open the flush king and let the black drain again. This time it will pull more contents out. Repeat this a total of 3 times and your saving water, using the gray water to wash out the black tank, and your black tank will be almost completely clean.
Another option is to use a toilet wand. You attach it to a garden hose, stick it down the toilet and turn the water on. It sprays all directions inside the tank. It's the same principle as the built in flushers, except you doing it with a wand.
If you do any of these methods of dumping, then yes, you can dump with less than full tanks.
If you don't want to do any of these methods, then definitely wait till the tank is good and full, then dump.
After dumping, add a bit of water to the tank (3 or 4 gallons), and then drive to your next destination. The water in the tank will slosh around and help clean the tank by beating up any solids left. Once at your destination, drain it completely and start all over using your tank.
Lack of water is your black tank's worst enemy. Be exceedingly free with water in your black tank. You'll always have a happy "potty" then!