Your resume gets out there, a recruiter submits you somewhere, trying to get traction. You submit yourself there and now you're attached to a recruiter (and his expenses) that you shouldn't be.
If you've ever put your resume up on a site like indeed, monster, etc. Then it's definitely been scooped up and put in a billion different job search engines.
But maybe you're fortunate enough to have avoided that mess.
If you publish something that isn't sharing it privately. If you provide your resume to a prospective employer or their agent (recruiters do NOT work for you) that is sharing it privately. If it becomes public as a result of you sharing it privately someone has been a jerk. IMHO beyond being a jerk their should be serious repercussions for publishing something without consent, inadvertently or deliberately. Something more than a minor business expense. Something like criminal charges against a person.
Of course it does. You may not work with them, but the companies you apply to do. They will pick up your resume and share it. Anything on your resume should be considered public information.