java.lang.IndexOutOfBoundsException: Source does not fit in dest

That's a very good question and it almost certainly has to do with the fact that setting a collections capacity does not necessarily allocate the underlying objects, but why are you doing it that way when you can just:

ArrayList <Integer> numbersCopy = new ArrayList<Integer>(numbers);

The constructor ArrayList(Collection<? extends E> c) will copy every elements from c into the newly created instance, thus copying numbers into numbersCopy. It is the same as numbersCopy.addAll(numbers) also, which is really what you need.

It does make sense that Collection.copy requires the dest array to be large enough to hold all elements from the source array. A similar analogy is the C function memcpy and the like.

Capacity does not equal size. The size parameter that you are passing in simply allocates enough memory for the size. It does not actually define elements. It's actually kind of a silly requirement of Collections.copy, but it is one nonetheless.

The key part from the Collections.copy JavaDocs:

The destination list must be at least as long as the source list. If it is longer, the remaining elements in the destination list are unaffected.

You should just pass the List to the ArrayList's constructor to copy all of the List to avoid the issue altogether.