Brent is describing exactly how things work at my club. A typical game is a four-ball, with everyone stroking off the low handicap in the group. Because it's match play, putts for bogeys and double-bogeys are often conceded, usually as irrelevant -- and scores above double-bogey are almost always irrelevant and get discarded when posting a score. But because we have to post every score in the US, regardless of whether you played medal or match play, you still have to do two things if you're an 8-handicap or below: (1) estimate what you would've gotten on each hole that you didn't finish; and (2) calculate your score where you take no more than double-bogey on any hole. That's the score you post into the computer.
When someone says "I shot 78," I know that he might've been conceded a putt or putts, and did his best to estimate whether he might've made them. At my club, when someone says that, it usually means they didn't have more than a double. Instead, someone might say "I shot 78 and posted 77," or something like that, in which case I know that means he made triple on a hole.
No one is under any misconception that a 78 in those circumstances is the same as a 78 in full medal play.