The dilution in your case is that each frequency is 1 millionth of the total power. If the total output was 5 volts at 5 ma, the total power output would be .025 watts so that each frequency would have a power of 0.025 / 1000000 or 25 nanowatts which in terms of zapping is negligible.
Also, a true white noise contains all of the frequencies in the domain, such as fractional frequencies 1.1 hz, 1.178 hz, etc. The number of frequencies can be infinite, theoretically, making the power at any one frequency infinitely small.