There were some people camping next to the base camp (you could see them through the window of your bedroom) so even if there wouldn't be any space, you could have done just that. Or were you so dumb as not to take a tent? :* And by the way, did you see a wreck of an airplane on the way to the base camp?
We did see the tents and yes, while we were enormously dumb for many things, considering how much I struggled as is - pretty thankful I didn't have to carry a tent on my back as well.