Gregersen: I can't help but side with the developer on this one. The hosting company can indeed disable things server wide that may be needed to run Updraft Plus. I have installed in numerous environments without issue, has have thousands of other people.
A few things to try. Disable all other plugins. There might be a conflict. If it still does not work, try changing the WP theme to the 2012 theme that came with WP. This will help to eliminate any errors caused by scripts that were installed with your theme.
If you still have problems I would advise talking to your hosting company to see if they have indeed disabled the scheduler.
I hope you can get it working because it really is a great plugin. I've tried a few others and Updraft Plus is the only one that has worked with every install.