c option (which is the default for both
minipage) doesn't center with respect to the baseline, but with respect to the formula axis, which is where fraction lines are, a bit above the baseline.
This is somewhat masked when the
\parbox has more than one line, but becomes evident when it has just one line.
Let's do an experiment.
$ $ % to activate math
Formula axis: \the\fontdimen22\textfont2
This will produce
Indeed, 5.97223pt minus 2.5pt is 3.47223pt and 0.97221pt plus 2.5pt is 3.47221. The difference in the fifth decimal digit is negligible and results from the roundings made by TeX to achieve machine independence.
You can get centering with respect to the baseline by lowering the resulting box by the height of the formula axis: