I agree that this is what the words appear to mean, but I think the two expressions are frequently used with the same meaning today - it fits me perfectly.it's the perfect fit = This one suits me perfectly. I will stop looking for another suit, this is the one.
it's a perfect fit = This one suits me perfectly, but I would like to see some more.
Your limb appears a wise place to be. The more I think about it, the less natural 'the perfect fit' sounds to me.I'm going to go out on a limb here and say that "the perfect fit" sounds odd whatever the context. I think you want "a perfect fit". Your new suit is a perfect fit.
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