Dan is right about that. However, this fail-safe thinking would only be needed if you have a backup of your website/mail/etc. ready to run on another hosting provider, in case DH should be down. If you have that, then you could "instantly" switch from DH to your backup provider -- plus the propagation time of the DNS change, of course.
For most of us, having DNS up without the hosting being up doesn't help us a lot, so it might as well be on the same provider.
The only problem I could imagine could be if DH suddenly closes up shop; then all of us one-basketers will be stuck. But I don't see that coming.
Try out DreamHost with a free WebID -- Prices, options