[AmityvilleHams]

To me it seems like you've encountered some extremely unsound dietary advice with this vet. Vegetables, especially leafy greens, are incredibly healthy and would NOT be contributing to weight gain and especially not to the level of obesity.

Even seeds and nuts in moderation are extremely healthy foods that hamsters should definitely be getting. That's a part of their natural healthy diet, and they provide valuable nutrients like healthy fats as well as important vitamins and minerals.

The idea that fat inherently leads to more fat being stored or created in the body is honestly a very dated one in humans and pets. Any food being consumed in unhealthily high amounts obviously won't be good, no matter the food it is, because dietary balance is important for good nutrition.

The thing that would really be unhealthy for hamsters in the long run would be added sugars, especially refined ones. These are generally found in low quality foods, but also many treats that are basically just pure junk food. They are nowhere near the same thing as the sugar content of a bit of carrot or even fruit(which many dwarf owners choose to avoid anyways) - these are processed added sugar with no nutritional value, completely unlike healthy fresh whole foods. This sort of thing isn't good for humans either or pretty much any animal for that matter though!