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The Align palette won't help in that case and – unlike InDesign for example – Illustrator currently does not provide an option to vertically align text in a text frame.
Sometimes a workaround is recommended (using the Convert to Shape effect), but that is probably not what you are looking for.
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Maybe too silly (especially if Kurt says so), you may consider A) in the following.
For (both horizontal and) vertical alignment of live Type, you can do it in one of the following ways, in either/all cases keeping the live (editable) Type (maybe simpler/better/more errorproof); you can make fine adjustments by eye with the transform effect if needed (goes for any solution).
The fine adjustments by eye may be relevant in some cases in much the same way as overshooting (also sideways as in the letters ID).
By the way, I believe that the explanation part should be corrected: it compensates for inaccuracies in human visual perception > it compensates for accuracies in human visual perception: what looks right is right.
A: In an existing box:
1) Tick Use Preview Bounds in Edit>Preferences>General;
2) Select the live Type with the (normal) Selection Tool and Effect>Path>Outline Object.
That will give you a Bounding Box that fits tightly round the live Type, and will ensure centring (both directions) and keeps doing so when you edit.
But if you need it as non outlined text in PDF you will have to remove the effect:
3) With the live Type selected, in the Appearance palette click the Reduce to Basic Appearance button.
That will bring it back to normal plain Type.
Obviously, you will need to untick Use Preview Bounds for other purposes, but you can just tick that again when you need to edit (some of) the Type if needed to keep it in place; that may not be necessary because the changes will (mostly, and only if no letters exceed the hitherto vertical bounds) be in the horizontal direction.
B: In a custom made static or automatically adapting box:
1) With the normal Type Tool create the text as live Type; you may wish to choose Align Center in the Window>Paragraph palette (bundled with the Character palette where you set the font and size);
2) In the Window>Appearance palette flyout click Add New Fill, then drag that fill down below Characters in the main Appearance palette and click it to have it selected; it will be highlighted;
3) Set the desired background colour (white), you may use the Window>Color palette or something else;
4) Effect>Convert to Shape>Rectangle (or Rounded Rectangle), then either:
4a) Click Absolute and set a predetermined size, or:
4b) Click Relative and set the width and height to be added to the live Type; you may try different values in Preview to see how it works.
This will give you the text as live Type so you can edit it (you may add text, even more lines), and it will stay centred on the background. If you choose 4a), you must keep the text inside, adjusting the font size if needed; if you choose 4b), the background will adapt to the text.