I agree, differential pairs only use series inductance, and capacitance between the two wire pairs to compute the impedance.
That said, on a PCB you form a "differential pair" but just running two traces close to each other. There is nothing to stop signals on one from coupling to another differential pair on another layer. do NOT run any of the differential pairs in parallel with each other for any long length!
Also, the ground plane top and bottom might have a loading effect on the differential pairs closest to them. You would need to calculate that effect, and maybe spread out the conductors a little.