From what I know cecotropes problems are frequently caused by diet. Rabbits under 3 months will leave cecotropes, but also rabbits having a diet which is too rich (the problem happened to my rabbits once when I went to my parents' house and had to buy a mix instead of regular pellets because there was nothing else - the issue resolved itself when I stopped giving them), obese / disabled rabbits who have a mecanical problem when it comes to grab the cecotropes, rabbits affected by GI stasis, rabbits who are so stressed out they interrupt their cecotropes eating regularly and leave them on the floor. Rabbits taking some meds like antibiotics. Generally giving the rabbit a lot of hay (regular hay like timothy which is not too rich) and stopping the pellets is enough to solve the problem. But in rare cases, rabbits affected by colibacillosis can stop eating their cecotropes. In this case cecotropes are often mucus-y and give an abnormal smell. It's probably what your vet diagnosed as you have to treat colibacillosis with meds (I might be wrong but it's the only case I know where a symptom like cecotropes problems is actually treated with something else than a change of diet / lifestyle) and the photos you've posted show unusual looking cecotropes. Antibiotics are given if it's caused by a bacterial infection. It's recommended to give vitamins to compensate the loss caused by the non-consomption of cecotropes. Eating them should resume when the colibacillosis is gone.
If you have a doubt about your vet, try seeing another. Having a rabbit is not enough to reassure me. Rabbit's guts are fragile and the cecotropes you show look really big to me, for a 4 month old, so I wouldn't just count on the problem going away on its own.
