The pups are offshoots from the main plant. I have a couple that will set seed underneath. Seedlings start off as a single grass like blade, and stay that way for a few years. The pups start off much larger, and grow faster. Check out the Floridata page for needle palm, it shows a clump being divided.

Here is a link that might be useful: floridata

I agree with Jfacendola, needle palms are clumpers! They usually start putting out pups long before they reach fruiting age and the pups grow much faster than seedlings do!
-Alex

The survival rate for taking these pups off of Needle Palms is about 50/50 since some may not get enough roots taken with it when separated. I would suggest using Superthrive or another root stimulator regularly with every watering when doing this. Getting the root system going is the most important thing in separating these pups from the mother plant.