No, the inevitability of it being present in a nearby planet went way up if the probability of it moving from one planet to another planet is decently high - and not otherwise.
No, it doesn't. If the probability per year is 10^-15, then the probability over 10 billion years (10^10) is still 10^-5. (I mean, yes, over a quadrillion years the probability approaches 1.0, but I don't think that helps your position.)
You keep trying to say "but big numbers of planets, and big amounts of time" to make this idea reasonable. But it doesn't work. You have to deal with how low the probability actually is of it happening from one planet in one year. If that's low enough, you can't salvage it just by saying "billions of years and billions of planets".
...and you can't refute it by making up tiny numbers.
Statistics is hard and you can be fooled by big/small numbers. Until some reasonable estimate of the actually probability of an asteroid making it from one system to another (oh look! There's one in our system now!) you can't make conclusions.