Ron, Have a look at the following.
http://www.watlow.com/downloads/en/brochures/windin0909.pdf
This is watlow's Din-A-mite series of 4-20MA controlled SCRs. The 4-20MA signal to the SCR controls % on time of the SCR. The document shows how at 20%, the SCR would be on for 3 ac cycles and off for 12. 50% would be on 3 off 3, 80% is on 12 off 3.
I would take the clients "insisting" on meaning that the 4-20MA control signal would come from the PLC and be the output of logic in the PLC (PID loop, etc) as opposed to using a separate stand-alone PID controller.
Aren't most all SSR (solid state relay) actually SCR (silicon controlled rectifier) componnents? The SCRs such as the Din-a-mite have additonal circuitry built in to do the PWM control of the scr from a 4-20MA signal.