"It's the other way around. The absorption ends up as heat and efficiency of absorption depends on the relationship of half wavelength to say radius of part absorbing. "
It's the "Magnetic" portion at lower frequencies......It's the "Electro" portion at higher frequencies. At least that's what the standard on electromagnetic exposure says.....
For Radiation it only depends on the power density in the field you're exposed to. With radiation the energy shuffles back and forth between the E and H fields. Absorption depends mostly on size, with a given conductance. If the field is due to a transmission line(energy not otherwise radiated) a person in that field would suck more energy from the line as you indicated. High AC magnetic fields result from high currents and wires with large spacial separation. Objects within that field will have induced currents that depend on the conductivity of the object. As the frequency goes up, the conductivity limits the power absorpiton from the lossy transmission line. At high frequencies the limited conductivity supports the voltage for high power absorption from the lossy transmission line.