At one of my recent training sessions in Birmingham I was asked about the LinkedIn setting that limits who can request to be connected to you. This is an option that could be used to protect from random people on LinkedIn from sending an invitation request.
In your Privacy & Settings select ‘Communications’ and then have a look at ‘Select who can send you invitations’
As you can from the above screen grab the default is anyone on LinkedIn.
In our conversations in the training session, one of the attendees had been asked to provide an email address to connect even though the person was a 2nd level connection. This person probably had the middle option selected.
I can envisage issues with the non-default options especially if not all email addresses have been set in the profile with the non-default setting. Equally if an imported contact list did not have one of the email addresses that the person trying to connect had put in their profile.
Incidentally my advice to all attendees is to make sure that all of their email addresses are registered within their settings and that their work email address is set as their primary. Remember that only the primary email address is displayed to connections the others are hidden but can always be used to log into the account.