I have always wondered--is there a computer that can actually tell what colors were when a picture is scanned--or is it subjective to whoever is doing the job?

If you're starting from a grey scale file, no there isn't. It's going to be up to the operator.
There are Photoshop actions that will do a good job restoring lost color to scanned faded color photos, but even those are just approximations that need adjustment by the operator.

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