A Lesson in Physics
It's important to note that different items get imprinted in different ways, affecting the size of the area that can be imprinted. For instance, giveaways like sunglasses and stress balls are imprinted by using pad printing—basically a rubber pad stamps a logo onto the item. The shape of a ball limits the area that a pad can print on, it won't cover the whole ball.
This same idea goes for all products and printing methods. Sadly, promotional product companies have yet to figure out how to break the laws of physics.
One more thing to note is that while a product, like a custom koozie, might be 4" by 4", the imprint area will be smaller, like 3" by 3". This keeps your imprint looking crisp and clean.