Hacker News Reader

Most likely explanation: the ambulance attendant looked at your LinkedIn profile.

Attendant Google'd name of the patient -> clicked on LinkedIn profile. That would be enough to get them suggested to you.

On the drive to my location... makes sense.

You said you saw it a week later. He could've looked at your profile any time in that week to establish a viable connection between you two.

Why would it have to happen on the drive?

You could use it to find questions to check how lucid they are.

Equally they said something that piped the interest of employee to check after.