How to restore: https://panel.dreamhost.com/kbase/?area=2585
Steps for restoring data on your own :
cd into the hidden directory named .snapshot (it will not show up in any directory listing at all, but it's there)
Choose how far back you would like to go ( hourly.0 is one hour ago, hourly.1 is two hours ago, nightly.0 is one day ago, nightly.1 is two days ago, weekly.0 it one week ago, weekly.1 is two weeks ago )
Copy the restored file to where you want it. You're done!
>DreamHost does not keep automatic backups of your database specifically
Really? Where do they say that?
On every DreamHost plan we keep extensive back-ups of your data. Periodically our disk filers take what is known as a "snapshot" of the entire file system as it stands at that time. If you accidentally delete a file you need, contact support, and we'll try and recover the most recent version of it we can! We recommend you always keep your OWN copy of your entire web site at a remote location as well, but we'll do our best to make sure that's never needed. Our filers are completely RAIDed and hot-swappable so if any disk fails no data is lost, and we can replace the disk without any interruption of service! There is no additional cost for these backup features.
Doesn't exclude DBs there.