Recently, LinkedIn has been targeted by spammers or phishers. I've received emails with hot links to a web site purportedly run by LinkedIn, but when I forwarded the email to the LinkedIn administrators, they told me it was a fake. So I wouldn't assume that these invitations are really coming from the people they are supposedly coming from.
If possible, these invitations should just be filtered out automatically, like any other junk mail or spam. If they are legitimate, they should be sent to the invitee, not the list.