According to http://justdelete.me/ LinkedIn has been reported to send you emails even after you delete your account. I know one woman who kept getting invitation emails from another guy, even though he wasn't active on the site at all. She was so annoyed that (with her permission) I added her email address to my account so it would stop bugging her.
I deleted my account a couple years ago. I used to always get emails from people who were inviting me to join. The emails were from invitations@linkedin.com but contained the name of the person in the subject. The message also contained text that looked like it was from the person:
On March 14, Person X wrote:
> To: bhelx [bhelx@example.com]
> From: Person X [personx@example.com]
> Subject: Invitation to connect on LinkedIn
> bhelx,
>
> I'd like to add you to my professional network on LinkedIn.
>
> - PersonX
The worst thing is I would get follow up emails "Reminder about your invitation from Person X" pretty regularly. I would unsubscribe using the link at the bottom of the email but I found that it was only unsubscribing me from receiving the follow up "reminder" emails from each person I unsubscribed from. It was really frustrating. I assume Linked In was explicitly requesting permission to do this.
It's not like Gmail adds a link to unsubscribe from all Gmail users' emails. If a user sends a message, LinkedIn can deliver it without falling afoul of CAN-SPAM.
LinkedIn is sending the emails. Even if someone intentionally put my email address in a box on LinkedIn and said "I'd like to connect with this person", if I've explicitly said I'm not interested in creating a LinkedIn account and not interested in receiving invites, then it is LinkedIn's responsibility to not send that email.
LinkedIn is not an email provider, they have no obligation to that user to send me a message.
That sounds broken. If I want to spam someone, I just need to set up a website that allows you to message users and then register for it myself and keep requesting to send messages. That sounds like the sort of obvious loophole you catch early on.
I've had this happen with Spotify. I connected my Facebook account and after a while I unconnected it, yet it still tells me to add people that I'm friends with on Facebook.