Acquired CCI due to inflammation has to work through remodelling of bone or ligament. If the remodelling is purely ligament then it will only lead to instability if there is rupture.
On the YouTube presentations of Dr Fraser Henderson and Dr Paolo Bolognese (the two leading CCI surgeons in the US), they talk about ligamentous laxity being the cause of the CCI cases they see.
From the "student notes" I made from these videos, in
this 2012 video at 13:12, Dr Henderson says says there are three components to diagnosing craniocervical instability:
1 — Clinical: the presence of cervical medullary syndrome (symptoms: headache, neck pain, visual changes, photosensitivity, hearing loss, tinnitus, hyperacusis, dizziness, vertigo, imbalance, dysarthria, word finding difficulties, dysphagia, choking, dyspnea, disordered CO2 regulation, sleep apnea, disordered sleep architecture, loss of REM sleep, gastric reflux, nausea, vomiting, IBS, weakness, spasticity, tremors, jerking, clinic movements and dystonia, sensory loss, hypersensitivity, RSD, Raynaud's, memory and cognitive issues).
2 — Radiological (MRI scan): metrics of instability, pannus, syringomyelia, spina bifida.
3 — Etiological: a reasonable explanation for ligamentous instability (such as inflammation, rheumatoid arthritis, lupus, infection, etc).
So they think infection or inflammation can cause the lax ligaments that lead to CCI/AAI.