I never heard of that, you can put them over a shower if you use shower trim

Could be a local restriction. I'd ask him for a reference. You can always call your local building department for clarification. Just tell them you're getting conflicting information and want to know the specific requirements for bathroom lighting, especially any restrictions around sinks. and also ask them for a reference. NEC (National Electric Code)? Local amendment to the NEC?

The only thing I'm restricted to is lighting in and around bathtubs and showers. Fairly standard stuff.

If your sink is next to the tub, it might fall under restriction for lighting within 3" of bathtubs. But that restriction is for cord-connected lights (table lamp for example), anything that's dangling or hanging, like pendant lights, track lights, chain or cable swagged lights, etc. The idea is if you are standing in the tub and slip, they don't want anything electrical nearby that you might instinctively reach out and grab a hold of. zzzzZZZZZZAP!

There are damp and wet requirements, but again, none of those pertain to sink lighting. At least not in my locale.

"Damp" is required over the bathtub or in the shower if water spray won't hit it. "Wet" is required if water spray will hit it.

I'd call your local building department. Get some return on your local tax dollars.

Just my 2 cents but I put in 3" hollegens over my vanity, (3) 50 wattts, in an 8th high ceiling over a single sink 68" long vanity. There are 2 more lights in the room that come on with the same switch.
#1 causes monster shaddows
#2 really not enough light. It's ok for general lighting, only time I wish there were more is when doing face stuff.
I did put in sconces as well but they are also too tall for my short self to eliminate the ewww and eluminate the me! But the room looks great! ; )