This is actually a good question. So, the simple answer is... there isn't enough rust on the grill to cause any issues, unless the rust is flaking off in chunks and you eat those chunks.
There are many people that use cast iron pots to cook in. These also rust over time. When needed the pot is brought out of storage, a metal scourer is used, and the pot is scrubbed. After this the pot is washed with soap and water and is ready for use.
Cooking food in a pot will allow for more of the rust to be absorbed into the food in question than just laying your food on the grill.
What I do to clean my grill is, take a steel brush and give it a good rub to remove any loose debris. Wash it with soap and water. Give it a light coating of oil and it's good to go.
Hope this helps you.