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Actually strings have very few resemblances to value types. For starters, not all value types are immutable, you can change the value of an Int32 all you want and it it would still be the same address on the stack.
Strings are immutable for a very good reason, it has nothing to do with it being a reference type, but has a lot to do with memory management. It's just more efficient to create a new object when string size changes than to shift things around on the managed heap. I think you're mixing together value/reference types and immutable objects concepts.
As far as "==": Like you said "==" is an operator overload, and again it was implemented for a very good reason to make framework more useful when working with strings.
Isn't just as simple as Strings are made up of characters arrays. I look at strings as character arrays[]. Therefore they are on the heap because the reference memory location is stored on the stack and points to the beginning of the array's memory location on the heap. The string size is not known before it is allocated ...perfect for the heap.
That is why a string is really immutable because when you change it even if it is of the same size the compiler doesn't know that and has to allocate a new array and assign characters to the positions in the array. It makes sense if you think of strings as a way that languages protect you from having to allocate memory on the fly (read C like programming)