EDS is Ehlers-Danlos Syndrome for those who are unfamiliar with this term. EDS is a disorder of collagen formation and can lead to bone abnormalities. Basilar invagination is a softening of the base of the skull where either the first vertebra or the skull base can impinge onto the brain stem. This impingement is a type of Arnold-Chiari syndrome.
X-ray is not the gold standard to diagnose this disorder but is a good first step. An MRI of the base of the skull would be the next step.
Dr. Corenman