Yes, it happens, for a variety of reasons:
The company web site doesn't support an easy way of posting and maintaining listings
This may sound unrealistic but if you think about it, job listings websites are designed exactly for that purpose, and offer a far friendlier interface to post and more importantly keep track of and organize listings, and collect and archive resumes. Some countries may have specific regulations when it comes to collecting resumes, and it makes much more sense to make use of a job board that already follows them.
In most company websites I've developed such facilities were not asked for, and when I proposed them, the common response was "well, we are using careers site
foo and we are happy with it".
The company web site doesn't really have that much traffic
For companies that don't have much use of their web site other than simply having some sort of on-line presence, it makes much more sense to post their listings at a site where they'll be way more visible, especially from the job seeker's perspective.
The company doesn't want to directly advertise they are hiring
Several companies opt to post listings on job boards anonymously, and only reveal themselves at a later stage of the hiring process. Even if they do post under the company name, it's far less likely that their listings will be found by people who usually check their company web site, employees, clients and competitors.
Now, one could argue that for the first couple of reasons it would make sense to post a listing in both a job board and the company web site. Well, that's really a question of cost, effort and value, in some instances it makes sense and in some it doesn't. If the job board provides an API or any other easy technical way of accessing your own data, the cost and effort are significantly smaller, as most of the process is automated.
In conclusion, it's not unreasonable for companies to only post listings in job board sites and you shouldn't really worry about it.