Hmm... Well, I'm not in university and haven't yet reached a point where I've had an interview for a software development position, but I really don't think the concept of hand-writing code for exams is very intuitive. There are other ways to prevent cheating and encourage students to remember proper syntax. For instance, students are to use school-provided computers without internet access or IDEs and type code in Notepad under supervision. This would be much easier for the instructors as well, because they can just copy-paste and compile the code in their IDE of choice...
I do understand the reasoning behind it, however. I do feel that a lot of programmers rely too heavily upon IDEs for code-completion, error-checking, and debugging. For a long time, I was one of those people. One day, I decided to download MinGW and use Notepad + the command line to compile my C++ code. I was amazed by how much I learned in the process of weaning myself from Codeblocks for a while. I did the same for HTML5/JavaScript and MXML/ActionScript3. Just Notepad. Whenever I made a mistake that caused a bug in the program (most often, I left out a comma or semicolon where I needed one), I manually went through each line of code to see if I could uncover the cause of the error. And I learned a valuable skill. Debugging; without having to rely upon my IDE to tell me which line I messed up and why. As a result of this experiment, I've become far more meticulous when I write code, making fewer syntactical errors than I had beforehand.
In short, I agree with Bregma in that students should be tested on their ability to write production code. On a computer, as it's more commonly done these days (I use pen and paper for diagrams, flowcharts, and other forms of graphical prototyping ).