I agree. It is not as simple as "gravity", but the host of problems that must be solved before we can even change the trajectory of asteroids made the answer of "gravity" good enough. At least back then. Now with reusable rockets a reality and access to space becoming cheaper before the turn of the decade it may be worth giving it a few whirls.
The right approach seems to be securing propellant. They are looking for water in asteroids to convert to fuel, but if they can land on an asteroid even throwing asteroid pieces on the opposite direction they want to travel at high enough speeds might do the trick.
If they can change the orbit of the asteroid towards earth, then slowing down, fitting the asteroid with thermal protection and find it a suitable spot to crash into might be doable. The trick is not to carry the propellant from Earth, but to somehow get from space.
And remember, asteroid crashes are 100% natural.