On LinkedIn you are not “friends” and they never send an email that says you are “listed as a friend,” as this is never done.
If you are not a member of LinkedIn you will not be contacted. The connection request is between members, not non-members.
When asking to connect to someone on LinkedIn you select the reason WHY you want to connect. . and one of the options is “friends,” and this option requires a person, your friend, to know your email address and enter it and actually click on ‘send’. . .LinkedIn will not do that.
If, as you write, you receive an email from someone asking to be friends on LinkedIn, or says someone has listed you as a friend on LinkedIn, this did not come from LinkedIn.
There are spoof emails from other websites that try and mirror LinkedIn and also spoof Facebook invites. . .so be careful.
If you are a member on LinkedIn, you can send a request to connect with another LinkedIn member and the connect request will be sent but it is not a request to be ‘friends,” as you will receive an email that says “So-and-So lists you as a friend and wishes to connect”