Did your friend check that live and switched live are not reversed? - In fact that all three fan connections are correct?
If you are absolutely confident that the wiring is correct, then I revert to my first guess that inductive coupling is upsetting the fan and making the lights glow.
Presumably you have GU10 led spots?
Here's a simple test you could do without interfering with any wiring:
Temporarily change one led lamp for a halogen lamp. If everything then works as expected that would prove my induced voltage theory correct. (In that sense your electrician would be right in blaming the wattage of the lamps). We are then back to needing a snubber.
On the other hand if the fan still runs uncontrolled then either the fan itself or its wiring are wrong.