Make sure that guides are showing. Select the table with the content tool. Hover the cursor over an edge, and shift it around until it changes to a double arrow. With this cursor icon showing, click on the edge. Sometimes this selects the edge, and sometimes it's necessary to try again while holding down the shift key. I look for a change in the measurement palette to see whether the selection is successful, but this is the old 6.52 measurement palette--it clearly shows when the edge, or edge rule, has been selected. Then command m to modify, choose the grid tab, and it should show just one edge that can then be modified.
I don't know if it makes a difference, but I tried this starting with the table tool settings at zero for the width of the frame and for the width of the grid (modify these settings by double-clicking the table icon in the tool bar, then clicking "modify" in the Preferences window that pops up). Probably with single cell tables you want to keep the frame at zero width--this is separate from the grid, and is more like a regular box where the sides can't be adjusted individually.