In my time working with designers, almost all of them refer constantly to these rules (esp. Fitt's, Hick's, and Miller's which basically reduce to "big buttons", "few choices", and "no memory required", respectively).

However, these laws are just constraints and trade-offs -- most of the time your competing candidate designs will follow them an equivalent amount. At that point, most designers don't reach for "proof", but rather for "evidence", e.g. user research studies.