What to do when a nurse writes initials in wrong spot?

I don't know what to do,but I think I did something wrong.There was a nurse working 12am to 7am and she put her initials in the box where I was supposed to put my initials. I worked 8am to 4pm. This went on for a week.I crossed out her initials and put my own,but I now know that was wrong.What do you do in your facility? I've don't it before with no problem.I'm in home health so its the same thing I guess.
I've was taught to add a footnote, and something along the line of "1. clarification, should read "JBN" for 0800 dose for 18-Sep-2012--JBN 09/18/2012" I was always taught you cannot cross-out or directly correct someone else's information as you should be initialling/dating corrections. But you can add a clarification, just like if the nurse before you transposed a medication dose you can put a foot note "1. Clarification, should read 1.5mL (1.5mg) as per MD order dated 09/10/2012--JBN 09/18/2012". My clarifications are always backed up in my narrative note/chart/nursing flow sheet as are the rest of my nursing interventions, treatments, etc.What has your clinical supervisor instructed you to do? What does your QA department suggest you do?