Great thread!
In hopes to clarify a tiny on fabric:
From all the examples you mention, the fabric is still in tension. Remove the internal pressure and the fabric crumbles. The internal pressure puts the fabric in tension.
Same for a car-tire and inflatoplane. If the internal pressure can't create tension, then the structure buckles.
I assume you wanted to say that a fabric structure can be loaded in a compressive manner, which is correct, but the differences between the statements are huge for us engineers ;)
PS: Not sure about what a swiss stingray is.