so was it the woman's fault that McD's was too cheap to buy cups that are quality?
Nope. But it was her fault that she didn't consider she was holding an extremely hot liquid in a relatively flimsy container and take the necessary actions to prevent an accident.
See, if I was handed a cup like that I'd immediately think (operative word here is think) man, this feels awfully hot and this cup doesn't seem real sturdy. I'd set the cup down to cool and perhaps even ask if there was another cup I could put it in or even if I could just have another cup to double up by putting the full one inside the empty one.
Of course that assumes the first time I noted a problem. If I had actually visited McD's before and received very hot coffee in a cup that didn't seem adequate, I'd probably stop somewhere else for coffee if I really thought it was a safety issue.
You take the necessary action to keep yourself safe, you don't walk mindless though life expecting others to look out for you.
McDonald's served hot coffee in a cup. Nothing more. The old lady dumped it on herself. The spilling caused the injury. Hot coffee itself does not inujure unless you put it on yourself.
If the bottom fell out of the cup, then you look to the cup. Was it meant to hold hot coffee? If so, the cup manufacturer is at fault. If not McDonald's is. But that didn't happen. She dropped it.
So did she drop it because of the quality? None of McDonald's other billions and billions of customers had an issue. The old lady f'd up and revealed a problem with the system (coffee served at too high a temp) - great, now they know and things change so next time some old lady can't hold onto a cup, no one has to hear about it...
...except the kid with the mop working the morning shift at McDonald's. 
In the end, it's an "is the glass half full or half empty" arguement. Does the personal responsibility lie in McDonald's to be sure they serve potentially scalding coffee or does it lie in the customer to make sure they don't pour scalding liquid on themselves. I happen to take the side of being proactive and making sure stuff like this doesn't happen to me rather than blaming someone else when it does.
Don't walk though life blindly expecting others to look out for you, then complain when they don't.