Disclaimer: My experience is with git rather than hg, but as I understand it the concepts apply equally to both systems.
An advantage of backing up to a remote repo is that if your local repo becomes corrupted (perhaps due to a problem with the underlying filesystem), that corruption does not get transferred over to the backup, unless the files in your working tree themselves are corrupted.
For example, it's possible for some of the objects in the repository, perhaps those which are rarely accessed because you don't change them, to become corrupted. It could be months before you use one of those files again, and so months before you notice (though I think doing a garbage collect run, eg git gc, will detect corruption).
So if you are backing up by pushing commits, you're creating an independent version of those objects, and using checksums (ie the commit hash) to verify the transfer of any new files. Whereas if you are backing up to a backup provider, you're duplicating the actual objects in the repo, in whatever state they are in, and duplicating any changes to those files, including corruption of them.
Usually backup providers will give you rollback (spideroak seems to be particularly good for this) but you'll still have to sift through a lot of versions to figure out when the corruption happened; also with some providers, the rollback period is limited (especially for free accounts).