All the answers here more or less say that's how interfaces are meant to be, they are universal public specifications.
This being the most discussed thread, let me post two excellent answers I found on SO when this question surfaced my mind.
This answer gives an example of how it can be nonsensical to have non uniform access specifiers for interface members in derived classes. Code always better than technical descriptions.
To me the most damning thing about forced public interface members are that the interface itself can be internal to an assembly but the members it exposes have to be public. Jon Skeet explains here that's by design sadly.
That raises the question why weren't interfaces designed to have non-public definitions for members. That can make the contract flexible. This is pretty useful when writing assemblies where you dont want specific members of classes to be exposed to outside the assembly. I do not know why.
