I've never pontificated in my life...

Ever!
I agree an AST requires exclusive occupation. Quite clearly (to me) the parents viewed the house as "theirs". They had exclusive occupation - their son didn't even have a key!
Alice has been asking questions on the landlordzone forum.
http://www.landlordzone.co.uk/forums/showthread.php?p=197297&posted=1#post197297
But what if they didn't have exclusive occupation? What if they occupy on a licence as lodgers? Does this really change matters? No. You don't need a tenancy for a property to be "let".
Let's look at a different scenario. X is a wealthy gentleman of quite some age who lives in Chelsea in a rambling house. He doesn't really like living on his own, so rents out three spare bedrooms to lodgers. He doesn't need money, the lodgers are children of friends. So he charges them £250 per month each. (Market rent would be, what, £1000++ pcm.) He declares the income on his tax return as it is above rentaroom. Eventually he sells the property at a massive gain.
Oops-a-daisies. Three lodgers means that he doesn't get PPR relief on the whole thing. But are you really saying that he doesn't qualify for 223 (4) relief? Or would you be trying to argue that because they were only lodgers then there was no letting?
Just going back to Peter D's reference to this having been closed down through dep relative relief. It's a wholly different thing. "Letting relief" is not really "letting relief", it is a part of PPR relief.