That's baloney. Feeding dry kibble is one of the biggest contributors to cats developing diabetes in the first place - that and overfeeding!
Lots of people here use timed feeders for their diabetic cats. And you can freeze portions and pop them into the timed feeder - that way the portions don't spoil. However, that said ...You do have a multi-cat household. When treating a diabetic kitty in the mix, you may have to think about making some changes in order to get that kitty well-regulated on insulin, because the food can either work
with the insulin or against it. It helps to think of your diabetic kitty's food almost as though it's "medicine," too. Amount of daily rations (based on his optimum/ target weight) is important, as is low-carb diet.
While your other cats may be accustomed to free-feeding throughout the day, this is counterproductive for your diabetic kitty if he has access to their dishes. (Him getting into contraband when you're not looking is never helpful to blood glucose control.)
Some others here with multi-cat households have found it helpful to start feeding all kitties, diabetic and non-diabetic alike, at the same times of day; if you give them a certain amount of time to eat at mealtimes (and you happen to have a few pokey eaters), after a few rounds of "the dishes are being pulled up, kitties; your mealtime is over," you might be surprised at how quickly they learn to eat at scheduled mealtimes.

(Believe me, no kitty will really allow himself/herself to starve to death, even if one is somewhat balky about the change a feeding plan in the household.) NOTE: Obviously, you
do need to make sure your diabetic kitty eats before you shoot the insulin ...
Hope some of these suggestions are helpful.