I found a way to make scanning on the HP 1315 work on Mavericks, though it wasn't very easy.
Basically I used the open source Linux drivers from HP itself together with SANE. It works very well.
I wrote my complete notes on this wiki:
This process can be made simpler, though, mainly by having a mavericks package for HPLIP http://hplipopensource.com/hplip-web/index.html
The above process can easily be mimmicked by more advanced users and developers to create a more convenient scanning app and sell it on the app store..