I think we wouldn't be in compliance with the spec which would probably break clients. https://github.com/wordnik/swagger-core/wiki/API-Declaration says:

    The basePath field is very important--while it's very common to have the Resource Listing and API Declarations on the server providing the APIs themselves, it is NOT required`

I guess it doesn't say specifically that it has to be fully qualified, but every example I've been able to find is.