When selecting the line tool and then trying to draw a straight line (I am tracing a drawing, by the way) instead of a straight line the area becomes a rectangle as if I have selected that section (as in, it's as if the line tool is not working). I'm not sure if I am supposed to click something else first in order to use the line tool correctly.
We are not able to reproduce the issue.Can you please attach a video describing the same??? Please make sure line tool in the tools panel(Keyboard shortcut "N") is selected before clicking and dragging on the stage.And if your object drawing mode is enabled you get a "selection rectangular bounding box" around the line after it is drawn.I hope you are not referring to that.If you could attach a video it would be great, then we can see the issue and help you better.
It looks like you are drawing a line in Object Drawing mode which will have a bounding rectangle. The rectangle will not be published in the final output but it is for selection purpose at the time of Authoring as stated by Sangeeta. You can trun off the Object Drawing mode in Tools panel by simply pressing 'J' key or click on button marked in orange in the below screen shot.
Further you can learn more about Flash Drawing modes here http://help.adobe.com/en_US/flash/cs/using/WSd60f23110762d6b883b18f10cb1fe1af6-7e8aa.html# WSd60f23110762d6b883b18f10cb1fe1af6-7e87a
Hope this helps.