Now you're making the same mistake with the time. Transform your clock into the same frame of reference you're using for length. Duh.
Really now, this is not difficult; why are you going out of your way to assume observers who can't manage to make all their observations in a consistent frame of reference?
Are you assuming (or concluding) that distance and relative motion add the way they do in Newtonian physics? That is observed to not be the case, on the scales and precisions of the GPS system.
In other words, the vector difference between the velocity of object B and C varies depending on the observer, and adding the same constant vector to the velocity of B and C changes the difference between their vectors.
New Salt Compounds Challenge the Foundation of Chemistry
The title is overblown (it depends on what you think the foundation is), but get a load of this:
And here's the philosophical bit:
The obvious example of local truth is relativistic effects being pretty much invisible over the durations and distances that are normal for people, but there's also that the surface of the earth is near enough to flat for many human purposes.
Any suggestions for other truths which could turn out to be local?