Can't add images to announcements in SharePoint-hosted app in Office 365

I tried something very simple:

1. Create a new SharePoint-hosted app
2. Add a new list to the app, based on the Announcements template
3. Deploy the app to my Dev site on Office 365

When I now add a new item (aka a new announcement) and try to add an image to the Body field, I encounter two errors (depending on whether I try to add an image from my Computer or from SharePoint)

Adding from my computer gives me an unexpected error:

Adding from SharePoint shows me a structure of all the apps in my hostweb, but no way to upload an image either to the hostweb or the appweb:

Is it not possible to add images to a Rich Text field in a list in an app?