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.
