You'd be better off sending your CV as a PDF, that way there are no 'corruption' issues.
I specially dislike that, but if you think about it nothing prevents them to copy & paste into a doc document (well, if they ask for an editable format may be they lack the skills to do it, who knows!).
My feeling is that it is just a business for them (as in not "helping me") and they will change anything in my CV (yes, lie; or worse: it will look like I lied) to get me an interview and get their share. The downside of this approach is that I will lose my time with a job interview I can't pass because I'm not a good match.
I know that not all agencies work that way, but some do.
Then again, an ODT is better than a link to a very sparse LinkedIn profile.