Can something (a particle?) arrive somewhere before it is sent?

I am watching a BBC program right now on the neutrinos that seemed to travel faster than light.
In it the presenter uses an example to clarify a certain possible phenomenon: a text message send to a person who is travelling in a space craft that is travelling close to the speed of light.
The receiving person, in the example, would receive the text before the sender had sent it probably using the new technique based on the newly found fast(er than light) neutrino and he even stated that if the receiver sends a reply back that the guy on Earth would receive it before he the Earth guy had sent the original, first one.
That goes beyond me.
Is that possible (theoretically)?
If so, can you explain that to me keeping in mind that I am not a physicist?