That's not a rumor, that farmer lady just confirmed that she HAD to so if she wanted to keep selling her milk.
Probably sheep and goat farmers have to do so as well.
The problem could be that if you take cattle that have been for generations supplemented grains, and been put on pastures with less than Ideal forage, then they may not produce optimal milk....though I would also question the laboratories baseline levels and called standards which may be entirely based on grain fed control groups. Sure it may have higher protein and other "nutrient" levels but it may also have higher levels of harmful elements as well...I simply do not have faith in much of what passes for laboratory nutritional science. Develop your own sense-ability and learn to go by taste and gut reaction.
Sheep and goats are a different animals, and if they have been bred to thrive on pasture and the pasture contains enough optimal forage the their milk shouldn't need any supplementation at all. Ive had purely pasture raised sheep milk and it is far richer in taste than any cows milk I know of. There are also a number of heritage breed cattle which do better in general on pasture without supplementation.