I have an obvious bias in this matter, but I think it's important to mention some experiences we had with third party hosts shortly after we released FogBugz 7. This was a pretty big architectural shift for FogBugz, meaning the IIS config was rather different.
As you may imagine, third party hosts run a lot of different software on their servers, which can require quite a few configuration changes not normally encountered. The more programs you stick in one IIS, the more changes you make, the greater risk that some component or another is going to stop working. When you get to the scale of a large hosting operation, it's less chance and more certainty that one app is going to be unhappy about another app.
Some of our standalone customers run into these issues as well, but less frequently. There's also more trouble diagnosing the issue. Large hosting companies are less flexible about reconfiguring and restarting their servers (for obvious and very good reasons) than independent groups. We provide support to the hosting company of course (they are our customer after all), but the turnaround time for issue resolution is just longer when we can't Copilot into the servers or run tests "after hours".
With the On Demand servers, we're pretty careful to only install software that works with FogBugz. :)