Pasting wiki markup into editor pane fails to convert

When pasting wiki markup into the page editor pane the editor fails to recognize and convert the markup. For example, here is the markup for a simple 3 line table:

|| Heading 1 || Heading 2 ||
| Left 1     |  Right 1   |
| Left 2     |  Right 2   |

After pasting this block appears in the html as

<p>|| Heading 1 || Heading 2 ||<br/>| Left 1 | Right 1 |<br/>| Left 2 | Right 2 |</p>

I expected instead to get a real table:

Note that pasting wiki markup in this JIRA form does the right thing. Pasting into a Confluence edit pane does not.