Do all dangerous asteroids first pass through keyholes?

Scitech Daily's MIT Engineers Devise the Best Way to Deflect an Incoming Planet-Killer Asteroid

Now MIT researchers have devised a framework for deciding which type of mission would be most successful in deflecting an incoming asteroid. Their decision method takes into account an asteroid’s mass and momentum, its proximity to a gravitational keyhole, and the amount of warning time that scientists have of an impending collision — all of which have degrees of uncertainty, which the researchers also factor in to identify the most successful mission for a given asteroid.

“People have mostly considered strategies of last-minute deflection, when the asteroid has already passed through a keyhole and is heading toward a collision with Earth,” says Sung Wook Paek, lead author of the study and a former graduate student in MIT’s Department of Aeronautics and Astronautics. “I’m interested in preventing keyhole passage well before Earth impact. It’s like a preemptive strike, with less mess.”

Questions:

1. Do all or at least most astroids that will pose a danger to Earth pass through a keyhole first?
2. If so, why? Why would previous but fairly recent close passes to some gravitational body be important for making an asteroid pose a danger to Earth?

For more on gravitational keyholes see answers to the following (and links therein)

• Gravitational keyhole for spacecraft flyby?
• Understanding gravitational keyhole analysis for Near-Earth Objects

as well as Wikipedia's Gravitational keyhole.