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However, the probability of the DNA getting hit would increase linearly with the amount of junk DNA, wouldn't it? So the chance of good DNA getting hit is exactly the same as without junk.

Not sure how it would help shielding the good DNA, unless it acted as a barrier.

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Mutations from radiation come from particles literally slamming into the DNA and screwing it up. The more spaced out the important parts are, the lower the probability that the particle hits a piece of DNA that’s important.

If I place 4 cups of water out in the rain, does their spacing affect how much water lands in each cup?

It depends on how you place them, horizontaly on a table no, in a pyramid yes.

I see what you're getting at, but in this example there would be millions of cups and the individual raindrops would be spread out over a massive area of land.

That doesn’t change anything. The probability an important cup gets hit is always equal to the surface integral of the rain’s flux across the important cup openings. Whether there are unimportant cups nearby doesn’t change anything.

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