Well, actually, at the time of adding the domain, they don't. Who "owns" a "site" is probably best described by the Whois information on file with the registrar, and really doesn't have anything to do with what you, or I, do when we "add a domain" under "Manage Domains" in the control panel
In other words, there is nothing at all preventing us from "adding" google.com as a domain under our account in the control panel (and, in fact, doing so generally won't hurt a thing - see the next answer for an exception to this ). The directory will be built under your account and a DNS entry made in DreamHost's nameservers, but the domain's nameservers are (hopefully!) not set to DreamHost's nameservers (they certainly aren't for google.com!), so the contents you load into that "domain's" directory on DreamHost will not be served to browsers using DNS to lookup "google.com" since the nameservers in use by google.com will have other IP lookup information.
Initially, nothing prevents it - and that is the exception I talked about in the first answer of my response. It does occasionally happen (there have been reports of this on these forums), and it takes contact with DreamHost support to sort it out.
Note that this cannot happen if the owner of a domain with DNS pointed to DreamHost beats everyone else in "adding" that domain in the control panel. This is usually what happens, but occasionally a user might register a domain, and point the nameservers to DreamHost's nameservers without bothering to add the domain to the panel - leaving themselves open to this (albeit temporary) "redirection" potential.
There have also been cases where a user had "added the domain" when he didn't own it and the actual owner runs into to trouble when he tries to "add" it - the Control Panel won't let him because it is "already in the system". Again, in either of those situations, it takes support to sort it out (and it is not hard to do, as the whois information authoritatively identifies the registrant).
I guess the lesson here is to always immediately add a domain to the Control Panel when you point DNS to DreamHost's nameservers (or even do it first). The chance that someone else has already done that is very small, and you can always check by trying to browse to it first, to make sure this hasn't happened. If it has, you can always report the situation to support and they can sort it.
Does any of that make any sense?