Why? Because a PID is a cycle time controller. It doesn't change the ON-state wattage of the element but just turns it on and off for specific periods of time. Units such as Auber's popular PID have a minimum cycle of 2 seconds. In order to run the mash maintain process as gently as possible, you'll want to be able to switch your element to "120 volt" mode such as what I did in my test controller so that when the PID is "ON" it's only 1375 watts.
Now, if the volume of wort inside the tube were larger, or the flow rate was sufficiently high, it would be fine to have a 4000w element firing, but I'm pretty sure that you'd caramelize the wort at typical RIMS flow rates. I'm not 100% sure so you can feel free to experiment.
I haven't created a pretty wiring diagram yet but here's the basic idea:
L1, L2, N, and G come into the box. That's black, red, white and green.
Now, the element has two terminals, one is wired through the SSR and then to common 1 of a DPDT switch (with center off) and terminal 2 of the element is wired to the common 2 of the DPDT switch.
source L1 goes to the A1 terminal on the switch and then you use a jumper from there to B1 on the switch so that L1 is routed to Element 1 in both positions.
source L2 goes only to switch terminal A2 and source neutral goes to switch terminal B2. This is basically what determines the element's voltage.
The switch has to be capable of 30a at 240v so the best one I found for this is Bryant 3025.
If you want, you can also move the "element off" function to a separate switch or contactor, and then you'd only need a SPDT switch for the voltage select.
Of course, make sure your green wire goes to everything metal that may be isolated for some reason..
Use GFCI outlets or breakers.