Tapping the brakes is almost definitely going to be better than not tapping the brakes.
Using the brakes causes the static friction between your tires and the road to increase; which slows down the car more.
The issue is that when the grip between the brakes and the tire is too strong, the coefficient of friction between the tires isn't high enough to maintain that static contact. This is when the wheels "lock up" and begin to skid. As you mention, kinetic friction is less than static friction, so wheel lock and skidding should be avoided.
This means that tapping the brakes is generally the best braking method in these conditions, as compared to not braking at all.
When considering modern vehicles, your friend missed the mark even more. Most vehicles sold now (as far as I know) have an ABS, an Anti-lock Braking System which actually disengages the brakes when they reach the threshold when you start to lose traction. Basically, you can push down on the brake pedal as hard as you want, and you can feel the brakes start "tapping" on their own, to prevent skidding, increase traction, and allow you to brake in the lowest space possible. Tapping is the method most cars automatically employ on icy surfaces, and if you try it for yourself (in a controlled environment), you will find that tapping the brakes should slow you down a lot faster than not pressing it at all; especially if you avoid skidding.
Hence,
Tapping the brakes is almost definitely going to be better than not tapping the brakes.
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