People seem to either have trouble understanding shared hosting or get upset that their accounts were disabled and don't tell the full story.
As with any shared hosting there's limits on what you can do on the server. The commonly advertized limits are space and bandwidth. But there's also limits against running servers or other persistent processes. This type of software constantly runs on the server eating up cpu time and memory regardless if someone's using your site. There's limits on how heavily you can bombard your mysql server.
For instance, people often don't realize that wordpress (by default) access it's database and makes the server render a new page every time a visitor clicks a link. This is great for a small site, it keeps updates published with out difficulty. The problem comes in when your site gets hit up with a lot of traffic. If a default wordpress installation got farked or digged it would probably crash the server. That's not fair to the other people on your shared server, so all hosts limit your CPU time use.
So yeah, you could use only 500mb of space and get your account disabled for using to many resources. Perhaps part of the problem is that DH doesn't set specific limits on the amount of CPU time you can use, or the number of connections to the mysql server. DH starts to limit things when you're adversely effecting the server or other users.
DH also doesn't just shut down your account if you use up to much space. They may well disable the website that's causing the problems while they contact you about fixing the issue. Support is happy to help you work through the issues and 'streamline' you website. There have been a few issues where a site started using a lot of resources, or has a huge spike in bandwidth and support subsequently finds content in violation of the TOS and then shuts down the account without refund.
As far as reaching actual limits with storage and then getting shut down, I don't believe that to be true. There are specific overage charges, and if you don't pay those DH may shut down your site. IIRC charges must be paid on the first of every month.
P.S. I think I'm going to have to start working on writing less in reply to your questions, I'm starting to look like rlparker.
art.googlies.net - personal website