It's all starting to come together. There's a great new video at The Chiari Institute's website. It's an hour long, but it's really helpful. Dr. Milhorat explains the connection between Chiari, EDS, and POTS. The TCI doctors believe there is a connection between Chiari and EDS forming together as birth defects, for a particular subset of chiari patients. The EDS can lead to POTS. With EDS, the collagen is not formed correctly, or there is not enough of it. Collagen forms the lining of veins and arteries. With EDS, they can weaken or lose their elasticity, causing POTS to occur. The veins aren't strong enough to keep the blood flow to the brain and the heart when upright.
That's how I understand it.
Update: The videos at TCI's website have been taken down. But you can read the article published on the topic here.