The article mentions a study from Switzerland [0] where the domestic rabbits would prefer eating the meat, which suggests they had access to herbivore feed alternatives.
Seems there's a bit more to it than just "Rabbit will eat meat before they starve".
It'd be very easy to test your assertion that the rabbits only eat meat because they are starving. Offer ten well fed rabbits meat, if they eat it then your assertion is false. Better yet, offer them the meat and their regular vegetarian food at the same time and see which one they prefer. My gut feeling is that more often then not they would try the meat.
