(It helped that there were three truly excellent cafes and a bunch of so-so ones within walking distance; this wouldn't work in, say, Silicon Valley.)
Notwithstanding my original comment, I make a point of leaving for lunch, even if there's food paid for by the company, including if I partake of the food itself. The break is important.
However, for some things, like an occasional small snack or a bit of caffeine-sugar water, it would be both a waste of time and of money to go out. Arguably, fiddling with a "free" coffee machine is also time-wasting.
For some, the severity of the interruption is more significant than the length of time or quantity of money involved. The variance in working style makes any one-size-fits-all policy questionable.
If your former boss made it very easy to get reimbursed for those trips out for coffee, his reasoning would carry more weight.