I understand that there will be some sort of capacitive coupling.
Yes, but capacitive coupling has implications that are even more essential than the name. Capacitive coupling implies that AC current will flow from the aggressor to the victim - via the parasitic capacitance.
And, whenever conductors are magnetically coupled - think parallel traces nearby on the board, or current loops coupling to each other - there will also be AC current induced in the victim, even if the coupling capacitance was zero.
Transformers work just fine with an electrostatic shield between the windings, after all, where the primary-to-secondary capacitance is approximately zero.
Now, if the victim had zero source impedance, then the DC current would not change the voltage. But no such zero-impedance circuits exist unless you're dealing with superconductors. As soon as the victim's impedance is non-zero, any current - whether DC or AC - will cause a voltage drop in the victim.
Furthermore, even if the victim was a perfect conductor at DC, it will not be a perfect conductor at AC, since at AC it's the mere geometry of the conductor that implies non-zero inductance. So, in all cases, AC currents will cause voltage drops across inductances in any conductor.
So, the physical explanation to all this is: practical circuits have non-zero coupling between all nodes, whether capacitive, magnetic, or both, and they have non-zero impedances. Thus currents flow from any node to any other node - we can name them aggressor and victim, but the nodes of course don't care about any of it. What matters, then, is limiting the magnitude of this coupling to keep the circuit functional.