You are correct. Print in webview will work when using the IE plugin, but it will never work with the AJAX. The plugin installs the ability for QlikView to access your Print in webview, but the AJAX uses regular internet security, which would never allow a website to access your Print or that would be a big security hole.
Plugin toolbar has indeed more options (like the Menu) that the Ajax does not, but this is not a bug, it's just that the Print works only in Internet Explorer (options like zooming will not work in Ajax clients).
Thanks and regards