You can certainly accuse me of overcomplicating something . . . or I can respond that the dive industry oversimplifies it.
Saying that a "no decompression" dive is a dive where a direct ascent to the surface (remember, it's got to be at a prescribed ascent rate, and may require stops) begs the question of what kind of dive it is when you have three teammates and no two computers agree on what the no-deco limits are.
According to the definition, if it requires a stop it's a decompression dive. Ascending, regardless of speed is still continuous upward movement, therefore, not a stop.
Example: A couple of years ago, Peter and I met our friends Ken and Claudette and Jaye at Casino Point in Southern California. We did three dives that day. The first one, we were pretty much all together for the whole dive, and nobody went into decompression, according to their computer. On the second dive, Ken and Peter dipped a few feet deeper than Claudette and I did, to look at a ray. At the end of that dive, which we finished together, Ken and Claudette showed no decompression obligation on their Aeris computers. Jaye had none on her Suunto. I had none other than minimum deco according to the way I run decompression. Peter had 20 minutes of deco on his Suunto! So, was that a no-decompression dive, or a staged decompression dive, or what was it?
Decompression is an individual event since each person can be effected differently, and is responsible for determining and/or agreeing to a particular dive plan. And each person buys and uses their own computer, tables, planned stops, etc. If that person's computer says that they've exceeded NDL's and now requires a stop(s), then that person is doing a decompression dive, regardless of what other computers in their group say. They bought that particular computer for a reason, if they're going to use it as a computer than they're stuck with what it comes up with. You know better than most that there are several different decompression models out there. Which one to use is up to the individual, either by direct choice through knowledge, or by default in buying a particular computer. As a team member you may have been stuck doing the deco-stop with him, but according to your computer you were not doing a decompression dive.
You can write a definition, but applying it to any given dive is going to show up these inconsistencies. Better to consider all dives decompression dives, and know what the deco you need to do for any given dive actually is.
If the dive plan you're diving has no decompression obligations/requirements, then you could accurately say that it is a no-decompression dive. Hence, the origin of the term. I don't need to consider every dive a decompression dive as a hard rule. Whether or not the dive is or isn't going to require deco-stops will be determined when the dive plan is made. Plan the dive, dive the plan, so to speak.