Ok, this is what I see happening:
/lib/yui/3.4.1/build/cssbase/base.css
th, td { border: 2px solid black; }
loads first and then:
/theme/styles_debug.php?theme=zebra&type=parent&subtype=base&sheet=core
th, td, a img { border-width: 0; }
loads second overriding the first rule. And unfortunately neither of these two rules are mine. One comes from Moodle core (YUI) and the second comes from the Base theme.
One thing you may want to do is add something to override that rule [td {border-width:2px;}] to the extra css box in the settings, or use the Moodle table built-in classes of r0 and r1 on your trs like this:
<tr class="r0"><td>data</td></tr>
<tr class="r1"><td>data</td></tr>
<tr class="r0"><td>data</td></tr>
And the theme will "stripe" them for you. As to the tds having their own border - that's going to either take a general rule (as I said above) or you can give the table a unique ID and then do a specific rule like:
#mytable td {border-width: 2px;}
So that it doesn't affect every table throughout moodle.
All that to say - neither of those rules actually come from Zebra, so you'd see this in any theme, so it seems that nowhere in Moodle do individual tds have their own border.