I experienced this same issue and found what I believe to be the cause.
I am the IT support for a company. I had recently reformatted a users PC and reinstalled Windows. After doing this I found I was unable to connect to that PC with LogMeIn. Her computer was part of our company domain.
I believe the reason I was unable to access her PC (and got that particular message) was because I had not yet logged into her PC physically...as in my account and desktop had not been created. I had never entered my credentials into her PC so it had no idea who I was. I found that when I used her domain credentials to login everything went fine.