Not really true. Depending on rabbit population, or if you have a goat, you can fairly straightforwardly maintain a lawn without mowing. You have to be happy with random rabbit carcasses / holes though. It does take some care (in regards to what you do with fertilizer) if you don't want weeds, but if you keep the land very barren, the only 'weeds' you'll get are wild flowers.

Obviously this all depends on drainage/soil type.