As Randy and others have pointed out, there is no explicit "shall" with regard to having a documented system. In terms of practicality, however, I don't know how you would fully control a design process without documentation. You may have discovered why documentation makes sense. If you couldn't demonstrate control to the auditor--show him that your system has requirements that control the effectiveness of the process--you're left with saying, "Trust me, it works," which an auditor is unlikely to accept as evidence.
On the other hand, if you can demonstrate that the designers understand the requirements and follow a standard process, the auditor would be wrong if he insisted on documentation.
Jim has captured the key points here. And reading that along with the excellent example smryan gives, should get you thinking.
If your process isn't clearly defined at the moment (and it sounds like it
might not have been if you couldn't convince the auditor), it won't be robust enough to cope with stresses, including growth - eg, in size, products etc.
But if it
is clearly defined, and your auditor is saying no, I want to see a written procedure, he's wrong. There is
no requirement for a documented procedure in 9001.
That said - one way of approaching it,
if you decide some documentation is necessary, is via a flow diagram, just setting out the main steps, decision points, and capturing what records are generated at which points (a good way to make sure you meet the requirements for records). A one-pager for example.
Finally - remember the purpose of having requirements in the first place! Because it's good practice, fosters a consistent approach, and enables both identification of problem points and improvement.