“The transformer can make significant distortion if loaded above 50%. That distortion can cause diodes and transformers downstream to become noisy”Sure. Harmonics are the result of distortion. The big nasty is the 5th harmonic (300Hz) which is the one that causes the problems. Any transformer will make more distortion as you put more energy through it, since they are inductive devices. Fluke Instruments published a paper on this topic back in the 1990s; I'll have to poke around to see if I can find my copy, but I think its online too. Here's one I found that deals with this topic in greater depth:
http://support.fluke.com/find-sales/Download/Asset/1260362_6001_ENG_K_W.PDF