I think the idea is that if you have a large-ish volume of old stuff--archives from old projects or documents or stuff that you won't need for a while--and it's already in Dropbox, tidy.io lets you offload that stuff into cold storage easily. That frees your dropbox from clutter (and space).
You might also see tidy.io as a nice gateway to Glacier. You don't need to reupload files or use a CLI.
Btw, Dropbox is built on Amazon S3, which has a pretty impressive SLA[1] and service-record. That's not to say that it has perfect uptime, but in general, issues with AWS have been availability issues, rather than durability. Both S3 and Glacier have really good data-durability guarantees(99.999999999%)[2], so I wouldn't worry durability within AWS. With backups, you don't care about availability nearly as much as durability.
[1] http://aws.amazon.com/s3-sla/ [2] http://aws.amazon.com/glacier/#highlights