He and Charlotte Brewer had (whether by accident or by design) positioned themselves so that I couldn't look at both of them at once

This happened to me in my interview too (Trinity, Cambridge, maths). The two interviewers sat at either end of a long thin table, and I got to sit half way along on one side, so I had to keep turning my head back and forth like a spectator at a tennis match.

I'm therefore inclined to suspect that it's a well-known deliberate tactic of interviewers, although (a) I'm not entirely sure what desirable thing it's supposed to achieve, and (b) I suspect two examples shouldn't make me that much more certain than one. (But then, I ditched the degree-level statistics course within a week of starting it, so who knows?)