That really isn't the case.
The card will run at it's normal speed.
However, it may be limited by the amount of data that can pass through an
AGP 4x slot.
In practise this is not normally a problem unless you buy the fastest AGP
cards on the market and even then their performance is way better than the
4x AGP would suggest.
AGP itself is still a very capable graphics platform even compared to PCIe
16x with the cards currently available.