You seem to justify it in your own little way... but this isnt acceptable.
Facebook is not the issue. Your insecurities are.
From what you have told us... she is telling you that you are controlling.. you say that you arent.
Without a doubt it is controlling.
You must be afraid that she will be tempted by other men. That she will see something that she likes, and prefer it to you. The healthy option would be to act like a man no women would want to leave.. your current behaviour is to pester her to go on the internet and confirm she is yours.
That is more a reflection on your self worth than hers.
I am sure most of the responses you have had on here thus far, and will recieve, will support that this as not acceptable.
Only by seeing this for what it is.. will allow you to move forward in a constructive and healthy manner