I would advocate a more nuanced position; that is, a project manager does not need domain experience IF his subject matter experts understand the risks and dependencies that are inherent to the domain.
Let's go through a couple of personal projects that I have been involved with where the project manager did not have domain experience.
The subject matter experts are so advanced in their knowledge of networks that they no longer understand what beginners (i.e. the project manager) do not know. They have assumed that when they indicate things to the project manager that he understands what they mean and will take appropriate actions.
The project manager is continually running into situations where he did not understand the implications of certain risks and dependencies. This has caused a certain amount of rework and delays.
Fortunately, this is not a project with tremendous amounts of risk or dependencies so the project will be late but will succeed.
Mobile Handset Project
Because the subject matter experts were not specialists, they knew most of the key principles of designing mobile handsets but did not understand all the nuances of handset design. There were several key issues required by practical handset manufacturing that were overlooked by the generalists and ended up creating such a strong cost over-run that the start-up went out of business.
SumaryIn the first project, the subject matter experts were extremely good, however, the project manager failed to understand the implication of some of their statements and this introduced large delays in the project.
In the second project, the subject matter experts were generalists and did not understand all the risks and dependencies of the project. The project manager (and start-up) were doomed to fail because "you don't know what you don't know". Both these projects show that a project can be delayed or fail because a project manager does not have domain experience.
However, if the project has complex uncertainties and/or dependencies then a good project manager without domain experience is likely to find himself in a position where the consequences of not understanding the uncertainties and dependencies will either introduce serious rework or torpedo the project.