The logic is this: when you bump two things together in a frictionless environment they change course. They didn't really need to do this to show that the asteroid would move. Maybe to find out how much it moved, but whether or not was never in doubt. But the unaimed arrow never misses, so it's easier to declare success by claiming they're gonna check and see if it moved when they moved it.
I'm not objecting to the test. There are things they proved: namely the ability to do it. Cool. But the major achievement here is providing proof for people who thought this was hard to do. Deniers and such.
To address your earlier question: a planet killer that's pointed at us just needs enough time because any impact will change its course, it's just a question of how much. The earlier the impact the less is needed.
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