Hey Moog,
I was experiencing exactly the same problem as you after upgrading to 2.6.
As you identified, the problem isn't in the uploading, but rather the wrong URL is linked (this is a database problem).
In my case, I poked around the code a bit and eventually found that an option in the database, upload_url_path, wasn't set. You can try my fix as follows:
First, lets see if your option is empty (or even there at all). You'll have to log into your wp database, but really you don't need to get your hands all that dirty:
SELECT * FROM wp_options WHERE option_name = 'upload_url_path';
In my case, the row was returned, but the option value was empty. To remedy this, you can simply:
UPDATE wp_options SET option_value = 'http://yoursite.com/path/to/upload/dir' WHERE option_name = 'upload_url_path';
If it happened to be the case that this directive wasn't stored at all (i.e. no rows returned on the SELECT statement above), I'm guessing you can just add it:
INSERT INTO wp_options (option_name, option_value, autoload) VALUES ('upload_url_path', 'http://yoursite.com/path/to/upload/dir', 'yes');
Well it worked for me anyways! =D
Best regards,
Chase