Yes, I would say it would be to convey the meaning that you want. To 'fit' a space suggests something matches a size of space rather than is able to be contained within it. The puzzle piece fits the space for it in the puzzle; a cat fits in the garage because it is only small and the building is larger.
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David Hattona cat fits in the garage because it is only small and the building is larger.I take it that was meant to be "car" instead.