Let me see if I understand this correctly...
The LAA has been given authority by the UK government to issue permits to LAA members to have the right to fly aeroplanes that the CAA doesn't want to deal with. As such members join the LAA and pay a fee, and then as such they have the right to have a permit for their aeroplane as long as they meet certain engineering / other standards, which the LAA inspectors determine.
Now the LAA has the right to expel any member for anything which the board feels is "prejudicial" to the LAA Ltd. And by expelling a member, I assume the Permit to fly is withdrawn and then than person may no longer fly their aircraft.
Would a post on a public forum like PPrune be considered "prejudicial" to LAA Ltd..? If so I would never post my real name IF I were a member (which I am not) because they have you over a barrel and their view may well be that it is prejudicial. Old boys clubs and all that ???