Is its Parent Directory writable by server?

I uploaded a copy of wordpress with my wp-config.php file correct, went through the process of adding my username, password, etc. and it seemed to work fine until I went to Import. I went to wordpress, it said I would need to upload the plug-in so I did. It said it was activated, but when I tried to click through it gave me the following message…

Before you can upload your import file, you will need to fix the following error:
Unable to create directory ../wordpress/wp-content/uploads/2011/06. Is its parent directory writable by the server?

I figured this might be a server issue so I called their help desk about what permissions the directory might have and they couldn’t tell me anything, instead they claimed it was a wordpress issue.

Is this actually a wordpress issue and if so, how should I resolve it?

Thanks!