We run into similar issue. When you open a file on Access Point (web), you are able to utilize the IE plugin (at least in QV 11), which renders the Qlik app in the same format as you see on the desktop. We also do this and prefer it.
However, when we open our apps in Google Chrome (which runs better in our organization because we are on a much older version of IE explorer), the Qlik app renders in the Full Browser Version, because I don't think it can utilize the IE plugin.
We have yet to find any solution to this unfortunately, and I believe support for the IE plugin may be going away.