FYI, if you are interested by understanding what happens, you can try this code :
{| class="wikitable"
|-
| The "wikitable" class paints a border around its table
|-
|
{| style="border: 1px dashed blue;"
|-
| style="border: 1px solid green;" | A border appears around this table, even
though I'm trying to explicitly turn it off
|}
{| class="plain"
|-
| The only solution is to use a "plain" style which does not paint a border
|}
|}
Actually the first style apply in to <table> and the second apply to <td>