I think the 'no seed' thing comes from those rabbit food mixes with seeds and fruit, being loaded with carbs, and that knowing that too many carbs and sugars can cause digestive problems for rabbits. But all rabbits are going to be getting carbs in their diets. All rabbit food has carbs in it, either from grain and molasses/fruit added to it, or from seeds. And if a rabbit is fed limited fruit as treats, then they are also getting carbs from that. So feeding black oil sunflower seeds or oats, really isn't any different. Feeding carbs and sugars just needs to be balanced and not overdone, or it can cause problems.
Also having a rabbit that has health problems and difficulty keeping weight on, you are also limited with what is going to help with that. There are only so many things that are going to help with weight gain with a debilitated rabbit. If the rabbit is having a difficult time eating enough to keep at a healthy weight, then you are going to have to try things that have more protein, fat, and/or carbs in less bulk. So even though feeding alfalfa is normally less desirable because of the higher calcium levels, if there aren't any preexisting bladder sludge issues, then it may be something that is necessary for certain rabbits, to help with weight gain, as it is higher in protein. The same goes for feeding the black oil sunflower seeds or oats. It's something that may be necessary for weight gain, for debilitated rabbits, but isn't something that pet rabbit owners normally feed. I would be more inclined to go with the sunflower seeds than oats, as they would be lower in carbs, but provide more protein, as well as fats from the oil. With the alfalfa hay, the earlier it was harvested, the more protein it will have. You want small stems, little to no flowering, and lots of good green leaves, for it to have the highest protein.
