Errm no, a reply-to header is not the same as a sender envelope. Spam filters will flag emails that are faking the sender envelope. Spf is also only checking sender envelope. A reply-to can generally be what ever you want, same for from header... So linked sends email with from and reply-to headers set with your email, but sender envelop is from their server. So email appears to come from you, but was sent from linked in server, which is setup to pass spf test so does not get flagged by spam filter. Check the headers in the emails raw source, and you will see what i mean

It appears the parent comment I was replying to got edited after I posted this. Thanks TylerJay for completely changing the meaning of your comment without any notice.

The original commented suggested that they sent the email themselves as if it had come from the user, not merely setting Reply-To.

That would only be true for only some recipients (by far not "everybody") only if Google's SPF record forbade other SMTP servers with -all. It doesn't, it uses ~all soft-fail.

Why? Precisely because of this: there are lots of perfectly legitimate situations when a third party sends email on your behalf.

Moreover, if LinkedIn signs their outgoing emails with DKIM, that would be a positive signal for a spam filter (and e.g. Gmail would show such mail as "sent via LinkedIn" or something to that effect).