Also, this happens whenever I copy and paste any text, say from a PDF or another program. This happens even when I set the stroke to none before pasting.
The blue stroke might be either of two things. I you haven't added any layers and/or changed the program defaults, the bounding box for frames is going to be light blue when in layout view. Does the line disappear when you hide frame edges (Ctrl/Cmd + H) or go to Preview mode? A frame edge remains the same size, too, when you zoom.
Since you said 2 pts it's more likely a real stroke applied by default. You can kill that by deselecting everything and checking that noo stroke color is specified, or the stroke weight is set to 0. It's also possible that the object style set for new text frames has the stroke defined (open the Object Styles panel and look for the style withthe little icon with the T inside -- by default it's Basic Text Frame, but it might have been changed in the template). If that's the case you can redefine the object style without the stroke -- probably not the best idea because it will remove the stroke from exisiting objects that have that style applied -- or you can change to a different object style for the default text frame (drag the icon).
Thank you, it did have to do with the default text frame setting, and I changed the default to none.