Subject: What squashed the plastic bottle - vacuum or air pressure

During a kitchen science birthday party my 12y-o daughter said I was wrong to 
say that there were two forces acting on a plastic bottle partly filled with 
hot water: internal partial vacuum causing shrinkage as hot steam condenses, 
external air pressure causing downthrust (?is that the right word?) on partial 
vacuum; she says there is only air pressure.  We are novices at science: who is 
right, and how can we prove it at home?  (For the purposes of the experiment, 
we ignored the softening effect of the hot water on the plastic itself.)

Re: What squashed the plastic bottle - vacuum or air pressure