On even the narrowest tire, the bead on the inside of the rim is only a few mm away from the brake pad on the outside of the rim. If the pad sits above the rim, it will wear enough to form a lip that can touch the tire bead.

On my 26" wheel mountain bike, with long V brake pads I have trouble adjusting the pad so that it doesn't extend past the braking surface. This is because the pad is so long that the rim begins to curve away from the pad. Some pads are curved to prevent this, but they aren't curved as much as a 20" rim is curved.