I missed the first post of this thread when I dug through the big backlog after being out of the country for nine days.
I still don't really understand the question.
I think part of this issue is explained by the JVC intry in the DecodeIr documentation:
http://www.hifi-remote.com/johnsfine/DecodeIR.html#JVC
JVC protocol has a lead-in on just the first frame, unlike most protocols with lead-in that have it on every frame.
As a learning remote tries to distinguish the one-time part from the repeat part, having lead-in on just the first frame can present complications. In many designs, it is important to have the boundary between one-time part and repeat part occur on a relatively large gap. In that case the one-time part must be lead-in plus the basic frame and repeat part would be the basic frame again. But if the learning code doesn't apply that rule, the one-time part may be just the lead-in and the repeat part will be the basic frame. That later form is what DecodeIr calls a pure "JVC" signal. Other patterns are distinguished from a pure JVC signal, but the documentation is intended to tell you to ignore such distinctions for ordinary uses of the decode (such as constructing a JP1 upgrade).
I don't know why that first signal looks like JVC but lacks the lead-in. Maybe it is a different protocol that is just too close to JVC for DecodeIr to distinguish. There are several hard to distinguish protocols similar to JVC. If it is another protocol that close, your results seem to indicate that the device can ignore the lead-in and then also can't distinguish its own protocol from JVC (you can use a JVC upgrade to operate that device).
Those signals are in-between Mitsubishi protocol and JVC protocol in timing, but much closer to JVC. If they were learned correctly, they match Mitsubishi, not JVC, in structure. I suspect the device would also accept Mitsubishi signals with the same numbers, despite the timing being closer to JVC. DecodeIr can barely distinguish JVC{2} from Mitsubishi, so if there is some third protocol in between, distinguishing it would be hopeless.