I like how BikeJournal defines things: one commuting day is defined as the round-trip from home to work and back. Just riding one way counts as half of a commute. And for those who are sticklers about non-"gratuitous" riding, there is the term "Most Direct And Safe" -- not necessarily the shortest possible route, but the shortest reasonably safe route one could take.

That said, I do like how the generally-agreed definition of commuting miles here on BF is whatever you ride between leaving home for work and returning home. Just as you might optionally run errands or take the scenic route in your car, so you ought to be allowed to count deviations from your MDAS route as part of your commute.

I hope the coworkers in question are also bike commuters; if they don't have a horse in this race, their judgments can be ignored.