The problem here is that under the sites admin - blogs - edit options you can change the permalink options but I believe there is no function here calling for the rewrite of the .htaccess file. Whereas if you use the settings permalinks page it is automatically coded to insert "/blog" as the base for your urls. So what we need to do is change the permalinks page to get rid of that extra coding. I explain how to do this below. I should note though that we are playing with fire here. And although this worked for me I'm a newbie to php code and can't predicate possible reprecussions.
The file you want can is:
wp-admin/options-permalink.php
if you want to get rid of that base name altogether delete or comment out the following lines:
82 - $permalink_structure = '/blog' . $permalink_structure;
92 - $category_base = '/blog' . $category_base;
102 - $tag_base = '/blog' . $tag_base;
if you prefer simply to change it from "/blogs" to "/site" simply replace "blog" in all three lines with "site"
This has changed the actually operation of the site, now we have to change the way the permalinks option page looks to reflect what it is actually doing.
to do this find the following line:
185 - <?php if( constant( 'VHOST' ) == 'no' && $current_site->domain.$current_site->path == $current_blog->domain.$current_blog->path ) { echo "/blog"; $permalink_structure = str_replace( "/blog", "", $permalink_structure ); }?>
Here you need to either delete or comment out JUST THE LAST PART of the line name: { echo "/blog"; $permalink_structure = str_replace( "/blog", "", $permalink_structure ); }
or again to change from using "blog" to using using "site" replace BOTH instances of "blog" with "site"
repeat this same process with the follwing two lines, but notice that on these two lines the code in question comes in the middle of the lines. Both the code before it and after it needs to remain untouched.
201 - <td><?php if( constant( 'VHOST' ) == 'no' && $current_site->domain.$current_site->path == $current_blog->domain.$current_blog->path ) { echo "/blog"; $category_base = str_replace( "/blog", "", $category_base ); }?> <input name="category_base" id="category_base" type="text" value="<?php echo attribute_escape( $category_base ); ?>" class="regular-text code" /></td>
205 - <td><?php if( constant( 'VHOST' ) == 'no' && $current_site->domain.$current_site->path == $current_blog->domain.$current_blog->path ) { echo "/blog"; $tag_base = str_replace( "/blog", "", $tag_base ); }?> <input name="tag_base" id="tag_base" type="text" value="<?php echo attribute_escape($tag_base); ?>" class="regular-text code" /></td>
Now you can upload the file to your site - go to settings - permalinks; change it to your desired permalink settings and save. Your site should now be working correctly.
Assuming you chose the comment out option the final code in options-permalinks.php should look as follows
82 - // $permalink_structure = '/blog' . $permalink_structure;
92 - // $category_base = '/blog' . $category_base;
102 - // $tag_base = '/blog' . $tag_base;
185 - <?php if( constant( 'VHOST' ) == 'no' && $current_site->domain.$current_site->path == $current_blog->domain.$current_blog->path ) // { echo "/blog"; $permalink_structure = str_replace( "/blog", "", $permalink_structure ); }?>
201 - <td><?php if( constant( 'VHOST' ) == 'no' && $current_site->domain.$current_site->path == $current_blog->domain.$current_blog->path ) // { echo "/blog"; $category_base = str_replace( "/blog", "", $category_base ); }?> <input name="category_base" id="category_base" type="text" value="<?php echo attribute_escape( $category_base ); ?>" class="regular-text code" /></td>
205 - <td><?php if( constant( 'VHOST' ) == 'no' && $current_site->domain.$current_site->path == $current_blog->domain.$current_blog->path ) // { echo "/blog"; $tag_base = str_replace( "/blog", "", $tag_base ); }?> <input name="tag_base" id="tag_base" type="text" value="<?php echo attribute_escape($tag_base); ?>" class="regular-text code" /></td>