Can Facebook tweet under my twitter account?

I am using twitter for quite a time and still was today caught by surprise to find (I even do not read my own tweets after all and twitter is very lousy for listing them back anyway) tweets under and from my twitter account proposing weight loss with a link to <truncated due to spam filter on this forum prohibits me posting some keywords>:

Are you serious <truncated due to spam filter on this forum>? Read this article ASAP! onlinepowernews<truncated due to spam filter on this forum>

Click to expand...

Except reputable and long used w/o problems apps like

• Disqus
• TweetMeme
• Tweepi by ThoughtPick
• etc.

I recently gave access to my twitter to:

• unfollowr stats
  <truncated due to spam filter on this forum prohibits me posting some keywords and links>
• shareaholic app
  <truncated due to spam filter on this forum prohibits me posting some keywords and links>
• DragonBlogger
  <truncated due to spam filter on this forum prohibits me posting some keywords and links>
• jwz
  <truncated due to spam filter on this forum prohibits me posting some keywords and links>
• The Huffington Post
  <truncated due to spam filter on this forum prohibits me posting some keywords and links>
• Mashable Follow
  <truncated due to spam filter on this forum prohibits me posting some keywords and links>

the access from the last ones I removed altogether now

Also I enabled recently added twitter functionality to connect to Facebook (under settings-->profile) which is supposed to write in only one direction from twitter to my FB account wall

So, what caused spam-tweets from my twitter account?

So, I left access to my twitter account only for Disqus

And spam-tweets continue to appear under my account

So, the Disqus is culprit!!!
And my tweets are being republished to my Facebook wall and some of my friends republish them on their walls
Very nice sef-foock

And what to do now? I mean whom to ask/consult?
Disqus is quite popular

I do not quite understand why in order to comment someone's blog I required to give not only read but also write access to Disqus?