An audience of one. What about on a piece of paper? In front of a computer. How would do in code reviews? You can state your concerns to the interviewer to see if they can accommodate.

I've never seen a whiteboard interview with only one interviewer. The smallest was 2.

Whiteboards are for diagramming things more complicated than lines of code. [e.g. Interactions between several web services or paths of control across entire programs]

I've honestly just accepted that by the standards of many people's interviewing processes I'm a bad programmer. :)

Yup. Hell, if you think you can do it, but you're put off by a whiteboard, I'll get you a laptop with a development environment on it and leave the room to let you work on the problem.

Interviews are stressful. Keeping the candidate relaxed should be on the interviewer's mind.