Not true. I just checked the headers on a recent email and LinkedIn is definitely setting the From correctly:
From: [redacted] via LinkedIn <member@linkedin.com>
The Reply-To is the one of the user however.
Even if the from address was that of the user who sent the message, it's kind of hard to ignore the huge LinkedIn branding the message resides in. You'd have to be a fool to miss it, because I'm pretty sure even a blind person's screen reader would pick up on this.
For the end user that isn't a member, they seem to not want to let you opt out of their emails.
Sometimes they get around filters by sending from different emails, that's really annoying. I should probably quit Gmail and go back to Cerberus which has awesome filtering!
Other networks (I'm looking at you, Facebook), instead trap you in using their interfaces to communicate with someone.
I think Linked-in is actually really protecting privacy in this respect.
Also, if the user grants you permission, you can see their email address within linked-in and avoid sending any communication through linked-in itself.