All I know is that when anyone talks to me over their cordless phone, there is loud annoying "buzzing" interference when they take their phone too close to any power source. Even holding the phone near a lamp or light switch gets noise.
My recommendation is to comply with the manufacturer's directives for best operation. Understandably, that is cumbersome in today's complex world where we have electronis everywhere, even in doorbells.
I'll let other electronic wizards explain the technical details, but my own _guess_ is that modern electronics are so small, light, and sensitive (using very low currents), that they become very sensitive to more power "stray" signals from other sources, especially older electronics that use more powerful internal currents. To keep the cost down of consumer products, there is no shielding.
I know of a hobbyist who has built extensive equipment in his garage. He took a lightning strike. His newest modern-day components were fried, but his old heavy-duty components weren't damaged at all.