It would depend on the assigment. Since he is a student, the motto "don't reinvent the wheel" does not apply here. He is there to learn how to do this stuff.

How else will he know how to modify somebody elses script which does not do all that is needed for a task.

Personally, it looks like he copied it and put his name on it. He didn't even rewrite stuff to suit "his" programming style.

Even in a work setting, can he put his name on it if he didn't do anything to the code?

When I was taking classes, I sometimes borrowed a snippet or two. I gave the authors credit and the professors didn't downgrade me. As one said, "you had to learn what the code does inorder to use it."

Your students case, I doubt he understands the code.

HEY! Why not make him walk through the code and explain it! If he can explain what it does, then you can lecture him on plagurism. If he can't then you can knock him for being a cheater.