It's not out of the mainstream with the USN Diving Manual, either.
I don't agree with the concept that, "just because it's the norm," we should use a term that's a little bit of a misnomer - or indescriptive of what's really going on. I believe that calling EAN "nitrox" for example (which is a nondescript term from air, which, too, is "nitrox") is also one of these misnomers. Ditto for the term "no-decompression diving" (as you mentioned), and even the term "waterproof" (after all, even submarines are "waterproof" only to a certain depth).
To me, the stuff that I put in my boats to make them go is "fuel" and not "gas," even though my boats have gasoline motors... 'Cause the stuff that goes in my scuba cylinders (they're not "tanks," which are what holds the fuel on my boats) is gas. Sometimes that gas is 21%, sometimes it's 32%, 50%, or 100% (which is a reference to it's active ingredient). To further simplify the system, my guys don't call it "21%" or "32%"... They call it by it's MOD - "70" or "20" or "120" or "210" or "190" or whatever. This really simplifies the whole process in my company, and refers to the only definitive difference between different gasses that matters.
Is that the norm? No... We find it hilarious when we go into a shop at a remote dive site and ask for a 210 mix and they look at us like we've lost our marbles.
PADI and the world calls it "DCS." Those in the medical community call it "DCI." Divers frequently call it "bent." The problem is, no matter what you call it, the term can't be defined by whether or not the diver exhibits symptoms or not... The affliction can happen even if the diver is asymptomatic, and does, in fact, happen to a small, asymptomatic non-problematic degree on every dive.
If you want to reserve the term "DCS" as only that bodily fizzing which causes a problem, then the issue is that the already complicated system of variables within an individual and from person to person is further obscured by whether or not the diver notices symptoms, whether or not he or she complains about it, and then whether or not the diver seeks or is even able to seek medical attention or treatment for the issue.
To analogize DCS to opening a bottle of soda, it's not fair to say that the liquid only bubbles if your hand gets wet when you open it. The reality is that the liquid inside the bottle always fizzes... And that, the more you shake it and the faster you open it, the more of a problem it's going to create. Using a computer (and various algorithms) to figure out exactly the point at which the liquid leaves the bottle explosively, drenching you and everyone around you isn't the point... And it's not much safer to know that exact point and go
right up to it and ride that line. It makes far more sense to simply minimize the possibility of it exploding in the first place. And it shouldn't surprise anyone who "rides that line" when the calculations are a bit off and yeah, everyone around them gets soaked.
So yes, I recognize that, within the diving community, the term "in-water recompresion" is generally a term reserved only for those divers who are exhibiting symptoms of DCI (excessive fizzing that is bad enough to cause issues), have been medically diagnosed with the issue, and are therefore being medically treated in the water in an attempt to minimize the size of the bubbles.
...But that's a misnomer, and, contrary to your insistence, is NOT "correct." The term "in-water recompression" means, "compressing in the water again" - no more, and no less - and does not preclude a medical diagnosis of DCI.
For what it's worth, the NOAA Diving Manual, which you refer to in terms of definitions, recommends that the procedure for a missed stop include the surface administration of 100% oxygen, not "in-water recompression." Ditto for all of the recreational dive agencies that I know of, and Diver's Alert Network/Duke Hyperbaric, who is clearly the world's leading authority on the matter. I can't imagine that the Royal Navy's manual says anything different, regardless of whether or not you consider what the OP did a "missed stop procedure" (which is what it was) or an "in-water recompression" (which is also what it was).
I see that none of the specifics regarding definitions matter. What I see is that the OP took on too much N2, needed more gas than he had to offgas safely, missed a whopping 30 minutes of staged decompression, then followed a non-recommended procedure for his missed decompression stop, even though every agency around recommends a specific procedure that includes only oxygen at the surface, and nothing about doing anything in the water. For this series of mistakes, the OP paid a penalty of zero - believe it or not, he totally got away with it - and now he's wondering what's wrong with his computer, which clearly wasn't the problem.
...Which results in you and I disagreeing about the specific definition of "in-water recompression," even though we both agree that the dive community as a whole generally has defined it differently than it's words suggest. I contest that the subject of definition specifics should not be the overrding theme of this thread... I think it obscures the useful parts of this thread.