In theory it would be quite easy to make a proxy site. I don’t think legally there is much GS can do if someone prints a set of coordinates on a different website. They have tried to stop the likes of c:geo many times and failed. It doesn’t use the API (which is what GS wants developers to use – it is horrid, esp the authentication)- but instead it parses the HTML page for a cache and prints the details in the phone app.
I think logging for caches can still be done without authentication (and hence non-members can log member caches) but this is something they could easily fix if it was to be abused.