No, tables are just plain confusing until you figure them out. Once, you do, they are amazing.
How did you set up the Borderless Table style? Did you select the table and turn off on the lines in Cell Options (which is cell level) or did you set the Row and Column pattern to alternative every other row, with all settings at 0 in Table Options (table level).
If you did the former, I think you are up against overrides. To assign the BottomBorder, instead of clicking, Right click the style and choose Apply style and remove overrides.
To visually see how I would set it up:
The table styles has all the rules turned off—in Table Setup, Row Strokes and Column Strokes.
The cell style has just to bottom blue line selected (rest are grey), then set up the rule.
Once they are both in place, click in a cell to assign the cell style with the bottom border.
Overrides can be a total PITA. Remove them—from the table in advance or plan on removing them as you assign the cell styles. To clear all overrides in a given table, select it and Alt/Opt click on [Basic Table] at the top of the Table Styles panel, and on [None} at the top of the cell styles panel. Then assign the table style, and if you are not using nested cell styles, assign those manually.
Thank you @BarbBinder! I was a bit dubious, but I went through everything in triplicate and I'm 90% happy with my table now. I understand a whole lot better now.
One difficulty I see with INDD's tables is that you can't see when overrides exist, or what the override is, unlike with paragraph styles that show the plus sign and the overrides in parenthesis. Also, I would never have guessed that one has to engage the strokes in the table style to simply nullify them.
I appreciate the time you took to help me out - you're a gem!