I'm using ArcMap 10.2.2 in a remote server and I have added the online "Imagery with Labels" base map to my map (first picture). When I turn it off the labels (and the light dashed line) remain visible though, and even by removing the basemap from the table of contents, they don't disappear (second picture). Why?
Some Basemaps add a 'Reference' layer with them, which is separate in your Table of Contents. Look in your TOC to see if there is a 'Reference' layer - it's added at the top of the order (so the labels show up on top of other features) and is separate from the imagery layer.