No it's not. Public photos are a privacy leak by default because anyone can copy and save them for their own sites. A well-know member of Xenforo did that to my own site a year or two ago. There is no way your members can get their photos deleted from that other site unless they issued a DMCA takedown. To save the drama, just have photos set as Members Only first this way members who want their photos public, will be responsible for their own actions. This makes the gallery equal or better than Facebook which lets you set the default privacy of their photos.
Another reason is that with the inclusion of RSS, all public posted photos can be fed into another site, blog or social networking site. That's great if you need it for the purposes of your own site, but if someone takes your feed and imports it into their own site all of your sites public photos will automatically go to their site and if a member ever deletes their public gallery, they can't get their photos deleted from the other site.