We give out a piece of javascript tags such as which site owners put on their site like http://exa
Yes, document.write can't be called from an asynchronously loaded script, because it's detached from the document, so it can't write to it.
You can see the approach used here for the google maps api to get around this problem. So, it is possible some of your 3rd party scripts that you haven't named, could have the similar callback pattern implemented.
https://developers.google.com/maps/documentation/javascript/examples/map-simple?hl=EN
Simple Map