I would say 'why take the risk'? She could be genuine but there are loads and loads of lovely Filipina ladies out there who wouldn't put you in this position. Even if the story was true. I agree with Tawi2, my experience my Pinay ladies is that they won't ask like this. There are certainly geniune exceptions but for 1) the story doesn't ring true and for 2) why take the risk for the reasons already given?
Seriously, anytime I've ever walked passed any 'computer shop' (what they call an internet cafe) in Manila, they are mostly packed with blatant scammers. They are in there all day, every day. I don't really blame them given the circumstance but what would hate to be on the other end of it!