URLs not working (?p=123) unless they’re fancy permalinks

Hello,

I am lost, not understanding a problem, could you help me, please ?

For some of my visitors,
On some browsers BUT not on all the browsers,
The URLs of my blog only work if they’re a fancy permalink : (root)/month/date/post-title (this is the way my blog is configured, to chose to display these fancy permalinks)
BUT if you enter instead a standard URL (root)/?p=123, for some users and some browsers it will load the right link, for some other users it will load instead the contents of (root), not the right post.

And the thing that is driving me mad is that this won’t be always the same browsers that don’t allow it to work, depending on the visitors >_<
In my case, the ?p=… links work only in firefox 2, 3 and Chrome, not in IE or depositfiles. For some other visitors, that works in Internet Explorer and Opera, but not Firefox ?!?

I made a poll, asking my visitors, if you want to take a look at the irrational replies :
https://poll.pollcode.com/6Yc3_result?v (the “random page” link the poll talks about uses the ?p=… structure)
(and in another poll, it appeared that 15% of my visitors had the ?p=… URLs not working)

Really, I am lost, here.
Could it be an htaccess problem ?
Or could it be linked to something else ?

I’m open to all suggestions, thanks a lot if you can help !

If you’re curious, here is the contents of my .htaccess file :

(root)/.htaccess

# BEGIN WPSuperCache
<IfModule mod_rewrite.c>
RewriteEngine On
RewriteBase /
AddDefaultCharset UTF-8
RewriteCond %{REQUEST_METHOD} !=POST
RewriteCond %{QUERY_STRING} !.*s=.*
RewriteCond %{QUERY_STRING} !.*attachment_id=.*
RewriteCond %{HTTP_COOKIE} !^.*(comment_author_|wordpress|wp-postpass_).*$
RewriteCond %{HTTP:Accept-Encoding} gzip
RewriteCond %{DOCUMENT_ROOT}/wp-content/cache/supercache/%{HTTP_HOST}/$1/index.html.gz -f
RewriteRule ^(.*) /wp-content/cache/supercache/%{HTTP_HOST}/$1/index.html.gz [L]

RewriteCond %{REQUEST_URI} !^.*[^/]$
RewriteCond %{REQUEST_URI} !^.*//.*$

RewriteCond %{REQUEST_METHOD} !=POST
RewriteCond %{QUERY_STRING} !.*s=.*
RewriteCond %{QUERY_STRING} !.*attachment_id=.*
RewriteCond %{HTTP_COOKIE} !^.*(comment_author_|wordpress|wp-postpass_).*$
RewriteCond %{DOCUMENT_ROOT}/wp-content/cache/supercache/%{HTTP_HOST}/$1/index.html -f
RewriteRule ^(.*) /wp-content/cache/supercache/%{HTTP_HOST}/$1/index.html [L]
</IfModule>

# END WPSuperCache

# BEGIN WordPress
<IfModule mod_rewrite.c>
RewriteEngine On
RewriteBase /
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule . /index.php [L]
</IfModule>

# END WordPress

Thanks a lot if you can help me !

Sabinou