“Private” is a platform label, not a universal technical standard. It may describe restricted access, a billing mode or another feature defined by the service.
Check the actual rules
Access, exclusivity, billing and recording arrangements vary. Do not assume that a label means no one else can access the session or that no record is retained.
A recording is a separate matter
Participation in a session does not automatically establish permission to distribute its recording publicly. A claim that a video is “officially released” needs a documented source or licence.
Keep live and archived material distinct
A dated recording is not evidence that a creator is live now. Pages should say clearly which format they describe, without presenting archived material as a current interaction.