Any electric appliance is subject to cast an electromagnetic field about it. I would assume the myth based upon speculation in that regard. And, I'd write it off too, but I've seen it at play before.
I bought a new 19" TV a few years ago, carried it home, set it up in the bedroom, set my digital alarm clock on top of it, plugged everything in and turned it on, and no picture on the top 2/3 of the screen. Didn't matter what I did to it. Was about ready to box it back up and carry it back to the store, when I ran across a small warning in the owner's manual that stated DO NOT place any LED devices (amongst other things listed), within X feet of the TV, because they emit an electromagnetic field.
I thought... No way, I had that alarm clock on top of the previous TV for years, and never had a problem. Picked up the alarm clock and sure enough, the TV worked like a charm.
Put that same alarm clock on top of my stereo in the living room, had ZERO affect on CDs, Tapes, or Radio signal. Put it on top of the DVD Player, didn't affect it all, even snuck it in on top of the TV in the living room, and it had ZERO affect on that one. Put it in front of everything to see if it would affect remote signals, and ZERO problems. All of which lead me to believe that the bargain 19 inch TV I bought, lacked protection against electromagnetic fields that the other equipment had.
If you're concerned, check calibration on your scale in several different spots under the light over your bench, if it doesn't affect it, which like the guys above, I'm gonna guess it won't; I wouldn't worry about it.
For the record, I have 3-24" flourescent fixtures above my bench, and I haven't seen any issues when I checked calibration on my scale.
BUT... I do have that LED alarm clock over my other work bench, and it might honestly be interesting to see what my scale does in the immediate vicinity of that clock.