I think many of those "Join my network!" emails are from people who imported their own...
...e-mail contacts into LinkedIn.
That's the only way people without a profile there could get those mails. Otherwise they'd have to be directly lying to those like Alex and Mike who deleted their accounts; not impossible, of course, especially if they don't actually delete an account but just make it "dormant". But then they'd offer you to re-activate it on the login page. (Facebook does something like that, don't they?)
And that couldn't explain Scott's experience. So it has to be people who have your e-mail address in their mail system importing them into their LinkedIn account, probably when they sign up for it.
That's the only way people without a profile there could get those mails. Otherwise they'd have to be directly lying to those like Alex and Mike who deleted their accounts; not impossible, of course, especially if they don't actually delete an account but just make it "dormant". But then they'd offer you to re-activate it on the login page. (Facebook does something like that, don't they?)
And that couldn't explain Scott's experience. So it has to be people who have your e-mail address in their mail system importing them into their LinkedIn account, probably when they sign up for it.