When linkedIn sends and email to you about adding someone to your network, the email appears to come from this person's individual email address (not something@linkedin.com). To me it doesn't seem like a 'reply-to' header either but perhaps i'm missing something.
Seems like it would be an immediate red flag to have their mail IPs sending out email from all sorts of addresses and domains. Is this because they have built up a lot of credibility with ISPs?