They get that from 210.11(B) and a healthy bit of "interpretation".
(B) Load Evenly Proportioned Among Branch Circuits. Where the load is calculated on the basis of volt-amperes per square meter or per square foot, the wiring system up to and including the branch-circuit panelboard(s) shall be provided to serve not less than the calculated load. This load shall be evenly proportioned among multioutlet branch circuits within the panelboard(s). Branch-circuit overcurrent devices and circuits shall be required to be installed only to serve the connected load.
Basically if those loads were evenly proportioned before and you add load to one circuit they are not evenly proportioned anymore.
You would have to provide a calculation that showed you did not overload that circuit.
