Their page clearly says: "All for what you so love github - on your server" and "Keep your source code at your server!"
That said. This project is really neat. It's not everyday that you find opensource projects with decent UI.
Or closed ones.
[edit] I just checked: GitLab stores issues in a database separate from git, therefore unless you have a solid backup plan for those, it will significantly increase the likelihood of you losing data. GitHub stores wiki pages at least as git objects, so when you clone your repository, you have a full backup of all of those.
If your team uses GitHub, you're paying a company to reliably store your data, and that's all the company does, and so I'm sure they have RAID0, plus backup drives, plus tape backups. If your team uses GitLab, you're hosting it yourself, so you are responsible for having reliable storage and backups. Obviously, it's infeasible for a tiny startup to have the same level of reliability that GitHub has.
palish's argument is that losing data is unlikely in either scenario. It's true that it's incredibly unlikely for both, but it's far more likely to happen if you roll your own solution. (It's incredibly unlikely that two values hash to one MD5. It's far less likely that two values hash to one SHA1. Either case is very unlikely, but SHA1 is magnitudes better.)
If you trust only local + gitlab, I would agree, you at are a higher risk than local + github. The point is, gitlab can be every bit as open and accessible as github, as to make it easy to have another account mirror your git repos. GitHub + free BitBucket private repos = cheap + reliable + redundant repos.
I can now have a local gitlab resource that I keep synced with repos in github, almost trivially. bliss