That sounds weird for sure.
Are you sure the projects actually are eclipse webtools projects and not just java projects ?
Any chance you are using maven and have not instlaled m2e-wtp which would be the part that makes maven projects into eclipse webtools projects if they use the right packaging/plugins ?
If you create a new Dynamic Web Project in an empty workspace, the default facets will be the highest installed in the workspace. if you then create an older server, for example 5.x, 4.x, 3.x, etc, the modules won't be deployable on that server and will not show up in the add / remove wizard. This is because the server only supports, for example, up to web 2.4, but your workspace created a web 3.0 project. The web 3.0 project is not deployable to an app-server that does not support that version of the spec.
This obviously isn't a problem if you create a web 2.4 project and deploy it to JBoss AS7.0 for example, since JBoss AS is backwards compatible with regards to jee spec. But it is an issue if you try to deploy a web 3.0 project to a server that doesn't support that version of jee.
The proper way to do this is to create the server first, then create your web project or ejb project or ear project. Targeting the project to the proper runtime will ensure the default facets are deployable on that server.