I would say absolutely not. It's happened to me, where I've given my racquet to someone to use, and they popped the strings right away.
I figure if the racquet had not been restrung in a while, then the strings were worn and they would have broke anyway.
Or, if the strings were new, then they somehow had to be defective, and they would have broke anyway
Basically, unless the person did something out of the ordinary, such that the strings would not have broken if a different person was using the racquet, there's no way I make him or her pay for the string job.
Now, I think out of common courtesy, the person who breaks the strings will often offer to pay for restringing. But, especially if it's a friend, it seems really cheap to take him or her up on the offer. Again, this is assuming they didn't do anything out of the ordinary with the racquet.