It’s obviously a bad situation to find yourself in, but it might be helpful to understand that, if the “files” in question involve possible copyright violations, it might well be illegal for DreamHost to “distribute” them back to you.
I won’t comment on the “rightness” or “wrongness” of any of that; copyright law in the United States, and much of the rest of the world has long been an issue where reasonable people disagree about what is “right” and what is “wrong”.
Considering how clear DreamHost’s TOS are about such things, it is a little surprising to me that people regularly find themselves in this problem.
It really doesn’t sound to me that this issue has anything at all to do with “DH reliability”. They didn’t “loose” your files, they removed them from their servers, and those are two very different situations.
As I have not seen your site, and do not have any personal knowledge of what was involved, I can’t really comment on that other than to say that it is always important to have your own backups of anything you place on a machine you do not own. Additionally, if copyright violations were involved, you loss of benefit from " all results of hard work of two sites’ staff for about a five years" is probably to be expected; it could be worse, as you could be being sued and/or prosecuted in addition to merely loosing access to those files.
At any rate, good luck in your attempts to resolve the situation.