The signature hack on the system is to reuse sprites mid-frame. That's the "racing the beam": after an object has been drawn, reposition the sprite to draw something else further down on the screen, before the scanline beam gets there.
Pac-Man didn't do that. Instead, it draws only one ghost sprite per frame, and flickers between the four of them every four frames. The flickering and racing-the-beam are opposites, not one causing the other.
Atari's programmers knew how to race the beam for reusing sprites. Air-Sea Battle did it years before Pac-Man. What's different about Pac-Man is that the objects aren't constrained in their movement. They can overlap on the same scanline which makes drawing multiples with a single sprite impossible. The right solution to this and what Ms. Pac did is smart sprite reuse - if they're on the same scanline, flicker temporarily, but then when they move to be separated vertically, race the beam to display both together. This didn't happen for Pac-Man because Atari rushed it to release in too short a timeframe to implement that, and also the code wouldn't have fit into a standard 4k cartridge and would have needed more expensive hardware with bankswitching logic chips. 2600 Pac-Man's terribleness was a business decision, not a technical limitation.