That's just it, SR doesn't require this, in fact, it says something completely different: That it is meaningless to talk about an absolute difference in clock rates. Dingle's claim of absoluteness of clock rate is something he brings into the argument which is not a part of SR.
No, Dingle says that they can't both be right and I'm saying that SR says that they can, you just have to adjust the way you deal with the concepts of time and space.
Dingle is like the people who used to argue against the idea of a spherical Earth on the grounds that the people on the "underside" would fall off. With a flat Earth model, "down" was an absolute direction and when introduced to the idea of a spherical Earth, some people just could not shale this idea. To them, a spherical Earth would have to have a topside and underside. They couldn't even wrap their minds around the idea that "down" could be defined as being towards the center of the sphere because that would mean that the direction of "down" changed and how could that be? I mean "down" is down and that is all there was to it. The idea that two people standing on different parts of the Globe could have their have their feet pointing in different directions and yet still both have their feet pointing down was impossible and a contradiction to their minds.
This is what Dingle is doing, he is clinging to a way of looking at time that has to be abandoned according to SR. SR isn't contradictory, it is just incompatible with his view on how time behaves.