So, while the computer is not your property, the information as well as access to personal accounts or information might be protected. All of that is personal and depending on jurisdiction can be protected and accessing it would be a violation.

I'm not entirely certain what the legal status of this in the US, but I know of other jurisdictions (Costa Rica, for example), where employers are forbidden from scanning, logging or viewing personal email accounts or even personal email on work accounts/computers. Hell, they can't even make a back-up of your computer without your permission.

source: Constitutional Court Prohibits Employers from Accessing Computers Without Employee Permission: http://www.elmundo.cr/sala-iv-prohibe-accesar-computadoras-f...

The issue would be more like "I see my neighbour left his door open when leaving for work; I go in, leave a note on the kitchen table and shut the door". This might be OK or not depending on community, but at least it wouldn't be always entirely unreasonable.