You are right, they are wrong. Running the board is extra. Period. The going rate in the LA area is $20-25 per show (tho you can negotiate more or less, as the case requires). If you signed your rider before negotiating this talk w AEA, but the fact is, you are supposed to be paid for doing any additional tasks. (And clearly your producers know this.)
Please point them to the section (54) of the SPT book that reads
J (8 ) Stage Managers or Assistant Stage Managers shall not be required to:
(a) Design, build, hang, transport, operate, shift, run, shop for or maintain lights, sound, scenery, props, video, wardrobe, animals,
and so forth;
AND
(D) Additional Services.
(1) Should a member of the Stage Management staff, while under contract for a production, be called upon to perform additional services
for any version of that production or for any other production in which the Producer bears a financial interest, the Stage Manager shall receive
additional compensation for such additional services in an amount which shall not be less than 1/6th of contractual salary for each day or part
thereof for which services are rendered. The Producer shall require no such service nor shall it be a condition of employment. (This provision
shall not prevent a Stage Manager signed to a Consecutive Production Rider, see Paragraph (F) below, from fulfilling rehearsal and
performance duties permitted therein.)
I have had two producers for whom add'l pay for running the board was a deal-breaker - so I made them hire a board op and it was a good think they did, since I had to do so many things during the show that I had to leave the booth on occasion to solve things backstage!