Wouldn't this be similar to using Photoshop or any other image manipulation tool? Adobe does not get ownership of output of their software. Why would we think some random website offering image manipulation would be different? As you say, the software is just a tool in the image creation process.
what gets really messy is the training data. Renaissance paintings are (hopefully?) all public domain, but what would be the case if I used living artists' work, or the collection of disney cartoons?
The pictures themselves are probably public domain, the photography of the picture however might be protected (photographer picked angle, lense, lightning, ...)
