Masses DO curve spacetime and thus can make clocks go faster/slower as well, but that is an effect described by general relativity, and one that is not relevant here. It could be added to this scenario, but you don't have to to get the twin-paradox.
I did not realize that,in principle, we were telling the same stuff
About above claim I am not that sure
Lets see
The special relativity plays of course a key role, in the twin paradox (Which is not pardox
) as well as in the particle accelerator experiments
However it is not exhaustive
Since the pilot comes back to the earth , the paradox entails an acceleration
The special relativity on the contrary assume a constant speed
The natural question is
What does it happen during the acceleration ?
In my opinion the explanation must be found in the Einstein's principle of equivalence , replacing the old Galileo's principle , i.e
Inertial forces == gravitational forces
The acceleration , regardless of the direction, is therefore equivalent to the presence of a mass ,which causes a further dilation of time, thus confirming the hyphotesi that the twin paradox is not a pardox but the plain truth
