I don't know who told you that, but that is BS.
People can draw their own conclusions, postulate and prove theorems. It is not necessary to be "told" something.
Fluorescents work by energizing the gas in the tubes. This generates plasma
This is a random process (see here).
All sorts of oscillations are produced. You can test that with any portable receiver. Keep in mind that the light from fluorescent lamps flickers, this means that the gas discharge starts and stops 120 times per second. Any non-linearity in this process guarantees that you get harmonics. It is pretty obvious that the discharge starts "all at once" - you can not feed 12V into the lamp and get it dimmer (at 10% of its normal output), this proves that the fluorescent lamp is a non-linear device. Any EE engineer should be familiar with characteristics of plasma-based devices.
The ballests, on the other hand, can put out interferance
The ballast inductor is a linear device. It can not put out anything beyond what is fed into it; however the lamp current goes through it, and all noise of that current will be emitted (poorly) via magnetic field. Ballasts usually have magnetic shields around them, but they won't be radiating much on RF bands. The bulk of microwave emissions comes from the plasma inside the lamp.
In fact, the filamets in incondesent bulbs act like large inductors, which act like very effective antennas.
The inductance of the filament is less than 0.001H, I fail to see how it can be called "large". Also, since when inductors became "very effective" antennas?
The only non-linear part of incandescent light bulb is that its impedance depends on the temperature of the filament. If the temperature stays more or less constant the lamp is as linear as it gets. They are commonly used as dummy loads to test transmitters.
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