Can a child get ptsd from something they saw on the internet?

Possibly. There is a lot of information on the internet, as well as graphic pictures. Children who are not supervised while using the internet may run across something unexpected and this could be confusing or troubling to them. To help avoid this make sure you discuss appropriate websites for them and keep the computer in a family area where you can supervise the usage.
Yes. I say yes. If a kid saw something so horrific, and something outside of the realm of a normal, human experience; the child could conceivably develop signs and symptoms consistent with ptsd. Studied have actually demonstrated changes in the brain following certain violent images. It depends on the content and the susceptibility of the child. We need to protect our kids and prevent such exposure.