Hi there,
Do you give them enough fresh food that they do not eat it all? Are they stashing it away? Or, are they eating it all in one meal and then not eating any of the other rat food?
Scattering the food all over the cage is not always good - it is hard for us to see where they did their business, and it is better to keep food in a central location for them to go and get. That way it is also easier to see how much food they are eating.
While fresh foods are great for rats, if you provide them with fresh foods all of the time, they will not eat the other foods. Usually in most cases, a good rat food mix is given as the primary source of nutrients with fresh food being treats given in smaller quantities.
It is likely that you may be satisfying their hunger by the fresh food alone, in which case they would not eat the dried stuff. Withhold the fresh food for a few days and see what happens? You might be giving them too much fresh stuff, and since it is scattered all over it is hard to keep track of how much they are eating.
They'll likely eat anything that they can find, rats usually eat whatever they can.
Good rat foods contain all of the essential nutrients that a rat needs, but it is still nice for them to get fresh veggies and treats to supplement their normal dried food intake.
Also note that regarding to proteins that giving rats too much protein can be bad for certain rats and they can get weird illnesses. They should only get about 10-15% protein maximum in their diet - my rats get a bit of chicken (a few small pieces) every week, but other than that they do not get protein. They get things like sweet potato, broccoli, mixed veggies, celery/cucumber/lettuce/spinach, apple/banana, grass, etc. a lot more than proteins.