I am an electricity neophyte here, so sorry if I'm mistaken or adding fuel to the fire, (just trying to understand).
Voltage is always with reference to something, right? So 120V per leg is with reference to ground, (and/or neutral, since they're bonded back in the breaker panel).
In this circuit, however, each 120V leg is not feeding to ground. The circuit is between a +120V leg and a -120V leg, so the electric potential, (voltage), is +120 - (-120), or 240V. If this switch were switching FOUR 120V elements, (two per side of the switch), each of which were running at (+120/0), then there would be 120V at each contact. But whenever one leg is at +120, the other leg is at -120, (since they are 180° out of phase), so whenever one leg is at +120, the circuit is going from +120 to -120, a potential of 240V. So in terms of arcing, 240V is the maximum voltage that could be driving an arc across the contacts.
Now since you're switching, presumably, with zero current flow, (this is assuming you have your PID turned OFF, I assume?), it's not an issue, since we don't care about arcing, since there's no current flow because the SSR will be in it's off state.
But if you did switch it while the SSR was in an on state, wouldn't there be 240V on the contacts?