The warning is done on a time frame where the ink is still present. Meaning, its becoming low and allowed to be run for awhile, you will have some ink, but it will become empty. If allowed to become empty it may dry out the ink cart to cause damage or need other corrective attention. You will get a feel for your needs how and when to replace the ink cart.
I have an HP Photosmart C6380, and it has been telling me I need to replace some of the ink cartridges. I have been ignoring the warnings and, for several weeks now, I have been printing both text and photograph pages with perfect quality. So I'm wondering if this is just the best they can do in monitoring the ink levels, or if there is a more nefarious motivation behind this "premature" warning to replace the carts.