I just realized that this "Cell Margins" button on Table Tools' Layout tab always shows (default?) margins for the entire table and not for a specific cell. Looking at the ruler, it is visually noticeable that the margins in different cells are different, but when I place the cursor in these cells and click this button, it always shows the same values regardless of what the ruler shows.

I found out that if you want to see the actual margins for a specific cell, you have to right-click the cell, go to "Table Properties" - "Cell Tab" - click on the "Options" button and here it is, a deeply-buried-but-so-much-needed-in-my-case dialog box called Cell Options (or is there a shortcut???). Here you can adjust cell margins as needed or just check "Same as the whole table" box. And the problem is solved.

Thank you once again, macropod