Not everyone is handling licences matters correctly. I don’t know the details of the MIT though. One thing, which makes StanHeaders special is that stan model binaries are created on the users machine. In turn everything stays source code only until one actually compiles and runs a model. That is a subtle difference which can become key.
Rstan itself must be GPL, since it uses RCpp, for example (but rstan cannot be used in R without RCpp baked in).