Technically true, this being APC where we play fast and loose with the facts when we wish to complain about something. However...

Apple programmed the iPhone to reduce performance when the battery reaches the end of its design life in order to prevent unexpected shutdowns. Before they did that, your battery indicator might read somewhere around 20% or more, but the phone could shut down while performing some processor-intensive task because the battery was unable to maintain required voltage in that condition under that load. This, obviously, leads to very unhappy phone users, whose belief that a 20% charged battery should last them at least a few more hours is not entirely unreasonable. So now, when your battery gets old, the phone slows down a little bit when it's working harder, ensuring that it stays powered on at lower battery charge levels, extending the useful life of the phone and its battery beyond the two years or so that it takes to run the battery to its charge cycle limit. If you don't want to upgrade, replace the battery, and you're back to full speed.

Under the current version of iOS (and might be one version previous to the current version), the performance degradation function kicks in (if I remember correctly from my recent experience with it) after the first unexpected shutdown, and not until then. You will receive an alert telling you that it has turned that function on. You have the option of inhibiting that behavior, maintaining full speed at the risk of experiencing unexpected shutdowns.