Given you're using a native .NET control, I think it's more due to file system permissions than the trust of the environment. If you were using a 3rd party control I'd say then it's a trust issue.
Having a quick look at Hostgator they use cPanel, from there there's the file manager section, and in here if you go and select the 'Photos'
folder and select "Change Permissions", here make sure the folder has write access from the application.
Edit
Support article here for setting *nix permissions: https://support.hostgator.com/articles/cpanel/how-to-change-permissions-chmod-of-a-file