FN is still in beta and the API is not documented yet, so apps haven't been written as far as I know. However I didn't say those apps existed, I said that such apps could be easily be written and that will very likely happen in the future as the site develops and matures.

I'm actually very interested in writing such an app, I'm just waiting on the website to be a little more solidified and the API documented before doing so. My app would need to "download" said pictures from FN to display them, so if the website disabled that then that art wouldn't be visible from 3rd party applications at all. :)

FN has an API which makes it very trivial for a program to download any content on the site. The idea is that people can write 3rd party apps to access FN (like say an iOS or Android app on your phone) and it would be extremely difficult for FN to enforce the "no download button" rule on those apps which are outside their control. Any protection schemes implemented through the web interface would require disabling API access to the same content, which cripples the API and prevents 3rd party apps from working fully, forcing everyone to the webpage and defeating the purpose of the API.

There are other solutions to curb reposting like watermarking and uploading low resolution images, which could be done by FN when uploading an image if the artist wants (put in an idea!). However an option to disable downloads would either be incompatible with having an API or be a completely false sense of security which only applies to the web interface, so I think it's less confusing to users to not have an option that doesn't end up really stopping anyone except the most lazy web-only users.